BITSAT PYQs for Differential equations with Solutions: Practice BITSAT Previous Year Questions

Updated 3+ months ago

Differential equations is an important topic in the Mathematics section in BITSAT exam. Practising this topic will increase your score overall and make your conceptual grip on BITSAT exam stronger.

This article gives you a full set of BITSAT PYQs for Differential equations with explanations for effective preparation. Practice of BITSAT Mathematics PYQs including Differential equations questions regularly will improve accuracy, speed, and confidence in the BITSAT 2026 exam.

BITSAT PYQs for Differential equations with Solutions

1.
If $f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12,$ then f(x) is
- increasing in $(-\infty,-2)$ and in $(0,1)$
- increasing in $(-2,0)$ and in $(1, \infty)$
- decreasing in $(-2,0)$ and in $(0,1)$
- decreasing in $(-\infty,-2)$ and in $(1, \infty)$
View Solution
2.
What is the solution of dydx+2y=1 satisfying y(0)=0?
- y=1-e⁻²ˣ2
- y=1+e⁻²ˣ2
- y=1+e²ˣ
- y=1+eˣ2
View Solution
3.
The expression satisfying the differential equation \[ (x^2 - 1) \frac{dy}{dx} + 2xy = 1 \] is:
- $x^2y-xy^2=c$
- $(y^2-1)x=y+c$
- $(x^2-1)y=x+c$
- none of these
View Solution
4.
Question: If |r| > 1 and
x = a + a/r² + a/r⁴ + · · ·,
y = b - b/r² + b/r⁴ - · · ·,
z = c + c/r² + c/r⁴ + · · ·,
then xyz is equal to:
- abc
- acb
- bca
- 1
View Solution
5.
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is
- $ y=\{\phi(x)-1\}+Ce^{-\phi(x)} $
- $ y\phi(x)=\{\phi(x)\}^2+C $
- $ ye^{\phi(x)}=\phi(x)e^{\phi(x)}+C $
- y-φ(x)=φ(x)e⁻φ(x)
View Solution
6.
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when $ y(1) = 2 $ is:
- ${none}$
- ${one}$
- ${two}$
- ${infinite}$
View Solution
7.
The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where $ f(x) $ is a given function is
- $ f(x) = x + c $
- $ f(x) = cx + y $
- $ f(x) = cx + y $
- $ yf(x) = cx $
View Solution
8.
The integrating factor of the differential equation
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:
- $\sin^2 x$
- $\dfrac{2}{\sin x}$
- $\log|\sin x|$
- (1)/(sin² x)
View Solution
9.
If $\phi(x)$ is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] is
- $y=\{\phi(x)-1\}+Ce^{-\phi(x)}$
- $y\phi(x)=\{\phi(x)\}^2+C$
- $ye^{\phi(x)}=\phi(x)e^{\phi(x)}+C$
- $y-\phi(x)=\phi(x)e^{-\phi(x)}$
View Solution
10.
The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of
- circles
- straight lines
- ellipses
- parabola
View Solution
11.
The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is
- $ \log \tan \frac{y}{2} + \sin x = C $
- $ \log \tan \frac{y}{2} + \log \sin x = C $
- $ \tan \frac{y}{2} + \log \sin x = C $
- None of these
View Solution
12.
Solution of differential equation \[ x^2-1+\left(\frac{x}{y}\right)^{-1}\frac{dy}{dx} +\frac{x^2}{2!}\left(\frac{dy}{dx}\right)^2 +\frac{x^3}{3!}\left(\frac{dy}{dx}\right)^3+\cdots=0 \] is
- $y^2=x^2(\ln x-1)+C$
- $y=x^2(\ln x-1)+C$
- $y^2=x(\ln x-1)+C$
- $y=x^2e^x+C$
View Solution
13.
The solution of differential equation 2xdydx-y=3 represents a family of
- circles
- straight lines
- ellipses
- parabola
View Solution
14.
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
- 194
- 1945
- 190
- 1940
View Solution
15.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
- 125
- 215
- 98
- 35
View Solution

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BITSAT PYQs for Differential equations with Solutions: Practice BITSAT Previous Year Questions

BITSAT PYQs for Differential equations with Solutions

1.
If \(f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12,\) then f(x) is

2.
What is the solution of dydx+2y=1 satisfying y(0)=0?

3.
The expression satisfying the differential equation \[ (x^2 - 1) \frac{dy}{dx} + 2xy = 1 \] is:

4.
Question: If |r| > 1 and
x = a + a/r² + a/r⁴ + · · ·,
y = b - b/r² + b/r⁴ - · · ·,
z = c + c/r² + c/r⁴ + · · ·,
then xyz is equal to:

5.
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is

6.
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:

7.
The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

8.
The integrating factor of the differential equation
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:

9.
If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] is

10.
The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

11.
The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is

12.
Solution of differential equation \[ x^2-1+\left(\frac{x}{y}\right)^{-1}\frac{dy}{dx} +\frac{x^2}{2!}\left(\frac{dy}{dx}\right)^2 +\frac{x^3}{3!}\left(\frac{dy}{dx}\right)^3+\cdots=0 \] is

13.
The solution of differential equation 2xdydx-y=3 represents a family of

14.
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.

15.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.

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BITSAT PYQs for Differential equations with Solutions

1.If \(f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12,\) then f(x) is

2.What is the solution of dydx+2y=1 satisfying y(0)=0?

3. The expression satisfying the differential equation \[ (x^2 - 1) \frac{dy}{dx} + 2xy = 1 \] is:

4. Question: If |r| > 1 and x = a + a/r² + a/r⁴ + · · ·, y = b - b/r² + b/r⁴ - · · ·, z = c + c/r² + c/r⁴ + · · ·, then xyz is equal to:

5.If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is

6.The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:

7.The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

8. The integrating factor of the differential equation \[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \] is:

9.If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] is

10.The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

11.The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is

12.Solution of differential equation \[ x^2-1+\left(\frac{x}{y}\right)^{-1}\frac{dy}{dx} +\frac{x^2}{2!}\left(\frac{dy}{dx}\right)^2 +\frac{x^3}{3!}\left(\frac{dy}{dx}\right)^3+\cdots=0 \] is

13.The solution of differential equation 2xdydx-y=3 represents a family of

14.If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.

15.If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.

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1.
If \(f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12,\) then f(x) is

2.
What is the solution of dydx+2y=1 satisfying y(0)=0?

3.
The expression satisfying the differential equation \[ (x^2 - 1) \frac{dy}{dx} + 2xy = 1 \] is:

4.
Question: If |r| > 1 and
x = a + a/r² + a/r⁴ + · · ·,
y = b - b/r² + b/r⁴ - · · ·,
z = c + c/r² + c/r⁴ + · · ·,
then xyz is equal to:

5.
If φ(x) is a differentiable function, then the solution of the differential equation dy+yφ'(x)-φ(x)φ'(x)dx=0 is

6.
The number of solutions of the differential equation \[ \frac{dy}{dx} = \frac{y+1}{x-1} \] when \( y(1) = 2 \) is:

7.
The solution to the differential equation \[ \frac{dy}{dx} = \frac{yf'(x) - y^2}{f(x)} \] where \( f(x) \) is a given function is

8.
The integrating factor of the differential equation
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:

9.
If \(\phi(x)\) is a differentiable function, then the solution of the differential equation \[ dy+y\phi'(x)-\phi(x)\phi'(x)\,dx=0 \] is

10.
The solution of differential equation $2x \frac{dy}{dx} - y = 3$ represents a family of

11.
The general solution of the differential equation \[ \frac{dy}{dx} + \sin(x + y) = \sin(x - y) \] is

12.
Solution of differential equation \[ x^2-1+\left(\frac{x}{y}\right)^{-1}\frac{dy}{dx} +\frac{x^2}{2!}\left(\frac{dy}{dx}\right)^2 +\frac{x^3}{3!}\left(\frac{dy}{dx}\right)^3+\cdots=0 \] is

13.
The solution of differential equation 2xdydx-y=3 represents a family of

14.
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.

15.
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.