Available Questions 44 found Page 1 of 3
Standalone Questions
#1484
Mathematics
Differential Equations
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Solve the differential equation $\frac{dy}{dx}=\cos x-2y$.
Key:
Sol:
Sol:
#1463
Mathematics
Differential Equations
LA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Solve the differential equation $(1+x^{2})\frac{dy}{dx}+2xy-4x^{2}=0$ subject to initial condition $y(0)=0$.
Key:
Sol:
Sol:
#1462
Mathematics
Differential Equations
LA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Solve the differential equation: $x^{2}y~dx-(x^{3}+y^{3})dy=0$.
Key:
Sol:
Sol:
#1431
Mathematics
Differential Equations
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation $\left[x\sin^{2}\left(\frac{y}{x}\right)-y\right]dx+x~dy=0$ given that $y=\frac{\pi}{4}$ when $x=1$.
Key:
Sol:
Sol:
#1385
Mathematics
Differential Equations
SA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following differential equation: $(1+x^{2})\frac{dy}{dx}+2xy=4x^{2}$.
Key:
Sol:
Sol:
#1384
Mathematics
Differential Equations
SA
APPLY
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the differential equation $2(y+3)-xy\frac{dy}{dx}=0;$ given $y(1)=-2$.
Key:
Sol:
Sol:
#1346
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Solve the following differential equation $x^{2}dy+y(x+y)dx=0$
Key:
Sol:
Sol:
#1345
Mathematics
Differential Equations
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation $\frac{dy}{dx}-2xy=3x^{2}e^{x^{2}};y(0)=5.$
Key:
Sol:
Sol:
#1322
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find the particular solution of the differential equation $(xe^{\frac{y}{x}}+y)dx=x~dy$, given that $y=1$ when $x=1$
Key:
Sol:
Sol:
#1321
Mathematics
Differential Equations
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation $\frac{dy}{dx}=y~cot~2x,$ given that $y(\frac{\pi}{4})=2.$
Key:
Sol:
Sol:
#1301
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
Competency
3 Marks
Find the particular solution of the differential equation given by $x^{2}\frac{dy}{dx}-xy=x^{2}cos^{2}(\frac{y}{2x})$ given that when $x=1$, $y=\frac{\pi}{2}$
Key:
Sol:
Sol:
#1278
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the general solution of the differential equation : $y~dx=(x+2y^{2})~dy$
Key:
Sol:
Sol:
#1277
Mathematics
Differential Equations
SA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation given by $2xy+y^{2}-2x^{2}\frac{dy}{dx}=0$ $y=2$, when $x=1.$
Key:
Sol:
Sol:
#935
Mathematics
Differential Equations
SA
APPLY
2023
Competency
3 Marks
Solve the differential equation given by:$$x \, dy - y \, dx - \sqrt{x^{2} + y^{2}} \, dx = 0$$
Key:
Sol:
Sol:
#919
Mathematics
Differential Equations
SA
APPLY
2023
KNOWLEDGE
3 Marks
Solve the following differential equation : $xe^{\frac{y}{x}}-y+x\frac{dy}{dx}=0$
Key:
Sol:
Sol:
#918
Mathematics
Differential Equations
SA
APPLY
2023
KNOWLEDGE
3 Marks
Find the general solution of the differential equation : $\frac{d}{dx}(xy^{2})=2y(1+x^{2})$
Key:
Sol:
Sol:
#917
Mathematics
Differential Equations
SA
APPLY
2023
KNOWLEDGE
3 Marks
Find the general solution of the differential equation \(e^{x}\tan y~dx+(1-e^{x})\sec^{2}y~dy=0\).
Key:
Sol:
Sol:
#916
Mathematics
Differential Equations
SA
APPLY
2023
KNOWLEDGE
3 Marks
29. (a) Find the particular solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}, y(1)=0$.
Key:
Sol:
Sol:
#915
Mathematics
Differential Equations
SA
APPLY
2023
KNOWLEDGE
3 Marks
Find the particular solution of the differential equation:$$\frac{dy}{dx} + \sec^{2}x \cdot y = \tan x \cdot \sec^{2}x$$given that $y(0) = 0$.
Key:
Sol:
Sol:
#815
Mathematics
Differential Equations
MCQ_SINGLE
APPLY
2023
KNOWLEDGE
1 Marks
What is the product of the order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}\sin y+(\frac{dy}{dx})^{3}\cos y=\sqrt{y}$ ?
(A) 3
(B) 2
(C) 6
(D) not defined
Key:
Sol:
Sol:
Case-Based Questions
CASE ID: #115
Cl: CBSE Class 12
Mathematics
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature.
A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that that the rate of reduction of its volume is proportional to its total surface area. Thus, $\frac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours.
SUBJECTIVE
REMEMBER
2025
AISSCE(Board Exam)
Competency
1 Marks
(i) Write the order and degree of the given differential equation.
(ii) Substituting $V = \pi r^3$ and $S = 2\pi r^2$, we get the differential equation $\frac{dr}{dt} = \frac{2}{3}k$. Solve it, given that $r(0) = 5$ mm.
(iii) (a) If it is given that $r = 3$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
OR
(iii) (b) If it is given that $r = 1$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
(ii) Substituting $V = \pi r^3$ and $S = 2\pi r^2$, we get the differential equation $\frac{dr}{dt} = \frac{2}{3}k$. Solve it, given that $r(0) = 5$ mm.
(iii) (a) If it is given that $r = 3$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
OR
(iii) (b) If it is given that $r = 1$ mm when $t = 1$ hour, find the value of k. Hence, find t for $r = 0$ mm.
Key:
Sol:
Sol: