Differential Equations - ISC Class 12 Mathematics Questions with Answers
50 past-paper questions on Differential Equations from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.
- Solve the following differential equation: $\frac{dx}{dy} = \frac{x}{y} + \frac{f(x/y)}{f'(x/y)}$ 2027 · 2 marks · Short answer
- If the solution of the differential equation $\frac{dy}{dx} = \frac{ax+3}{2y+5}$ represents a circle, then find the value of $a$. 2027 · 1 mark · Short answer
- Solve the differential equation $\frac{dy}{dx} + y \tan x = \sin 2x$, when $x = 0$ and $y = 1$. 2026 · 6 marks · Short answer
- The solution of $\frac{dy}{dx} - y = 1$, $y(0) = 1$ is given by: 2026 · 1 mark · MCQ
- Show that the general solution of the differential equation: $\frac{dy}{dx} = y \cot 2x$ is… 2026 · 2 marks · Derivation
- Solve the following differential equation: $x \frac{dy}{dx} = y - x \tan\left(\frac{y}{x}\right)$ (Application) 2026 · 4 marks · Short answer
- Solve the following differential equation: $x^2 dy + (xy + y^2) dx = 0$ 2026 · 6 marks · Short answer
- Find the general solution for the following differential equation: $\frac{dy}{dx} = (1 + x^2)(1 + y^2)$ 2026 · 1 mark · Short answer
- Find the particular solution of the following differential equation: $x^2 dy - (2xy + y^2) dx = 0$ given that $y = 1$ when… 2026 · 6 marks · Short answer
- Find the particular solution for the following differential equation: $\sqrt{1 - y^2} \, dx = (\sin^{-1} y - x) dy$, given that… 2026 · 6 marks · Short answer
- Solve the following differential equation: $(1 + x^2)\frac{dy}{dx} + 2xy = 4x^2$ (Application) 2026 · 4 marks · Short answer
- The integrating factor of the differential equation $(1 - x^2)\frac{dy}{dx} + xy = ax$ is: 2025 · 1 mark · MCQ
- The solution of $x\,dy - y\,dx = 0$ represents a family of straight lines passing through the origin. Justify. 2025 · 2 marks · Short answer
- Solve the following differential equation: $\cos^2 x \frac{dy}{dx} + y = \tan x$, given that $y(0) = 1$. Hence, find… 2025 · 4 marks · Short answer
- Solve the differential equation: $(x + 5y^2)\frac{dy}{dx} = y$ when $x = 2$ and $y = 1$ 2025 · 6 marks · Short answer
- An integrating factor of the differential equation: $x \frac{dy}{dx} + y \cdot P = x \cdot e^x \cdot x^{-1/2} \log x$, where $P$… 2025 · 1 mark · MCQ
- Solve the differential equation: $x(x - 1)\frac{dy}{dx} - y = x^2(x - 1)^2$. Find the particular solution satisfying the… 2025 · 6 marks · Short answer
- Consider the following differential equation and answer the questions… 2025 · 6 marks · Long answer
- A child is solving an equation $x^2 + y^2 = 1$ and finds that this is the solution of the following differential equation… 2025 · 2 marks · Short answer
- Solve the differential equation… 2025 · 6 marks · Short answer
- Degree of the differential equation $a\left(\frac{dy}{dx}\right)^2 + b\frac{dy}{dx} = c$ cannot be determined. Assertion (A)… 2025 · 1 mark · Assertion-reason
- Which of the following is a homogenous differential equation? 2025 · 1 mark · MCQ
- Find the particular solution of the differential equation: $(x + y)\,dy + (x - y)\,dx = 0$, given that $y = 1$ when $x = 1$. 2025 · 6 marks · Short answer
- Find the particular solution of the differential equation: $(x^2 - 2y^2)\,dx + 2xy\,dy = 0$, when $x = 1$ and $y = 1$ 2025 · 6 marks · Short answer
- Find the function ‘f’ which satisfies the equation $\frac{df}{dx} = 2f$, given that $f(0) = e^3$. 2025 · 2 marks · Short answer
- Show that $\tan^{-1} x + \tan^{-1} y = C$ is the general solution of the differential equation $(1 + x^2)\,dy + (1 + y^2)\,dx = 0$ 2025 · 2 marks · Derivation
- Solve the following differential equation: $x(x^2 - 1)\frac{dy}{dx} = 1$, $y = 0$, given $x = 2$ 2024 · 6 marks · Short answer
- Solve the following differential equation: $2y e^{x/y} dx + (y - 2x e^{x/y}) dy = 0$, given $x = 0$ and $y = 1$ 2024 · 6 marks · Short answer
- The order and the degree of differential equation… 2024 · 1 mark · MCQ
- Solve the differential equation: $(1 + y^2)(1 + \log x) \\, dx + x \\, dy = 0$ 2023 · 2 marks · Short answer
- Solve the differential equation: $(1 + y^2)\,dx = (\tan^{-1} y - x)\,dy$ 2023 · 4 marks · Short answer
- Find the particular solution of the differential equation given below: $(1 + x^2) \\, dy = (\tan^{-1} x - y) \\, dx$, given that… 2023 · 6 marks · Long answer
- Solve the differential equation: $(x^2 - y^2)\,dx + 2xy\,dy = 0$ 2023 · 4 marks · Short answer
- The degree of the differential equation… 2023 · 1 mark · MCQ
- Solve the differential equation: $\frac{dy}{dx} = \operatorname{cosec} y$ 2023 · 1 mark · Short answer
- The degree of the differential equation… 2022 · 1 mark · MCQ
- Solve the differential equation: $\operatorname{cosec} 3x \, dy - \operatorname{cosec} y \, dx = 0$ 2022 · 2 marks · Short answer
- Solve the differential equation: $\frac{dy}{dx} = 2 - y$ 2022 · 2 marks · Short answer
- Solve $\frac{dy}{dx} = 1 - xy + y - x$ 2021 · 2 marks · Short answer
- Find the sum of order and degree of the differential equation… 2021 · 1 mark · Short answer
- Form a differential equation of the family of the curves $y^2 = 4ax$. 2020 · 2 marks · Short answer
- Solve the differential equation $(1 + x^2)\frac{dy}{dx} = 4x^2 - 2xy$. 2020 · 4 marks · Short answer
- Solve the differential equation: $\frac{dy}{dx} = \frac{x + y + 2}{2(x + y) - 1}$ 2019 · 4 marks · Short answer
- Solve: $\sin x \frac{dy}{dx} - y = \sin x \tan\frac{x}{2}$. 2018 · 4 marks · Short answer
- Solve the following differential equation: $x \frac{dy}{dx} + 2y = x^2 \log x$ 2018 · 4 marks · Short answer
- Find the differential equation of the family of concentric circles $x^2 + y^2 = a^2$. 2018 · 2 marks · Short answer
- Find the differential equation of the family of curves $y = Ae^x + Be^{-x}$, where $A$ and $B$ are arbitrary constants. 2018 · 2 marks · Short answer
- The population of a town grows at the rate of $10\%$ per year. Using differential equation, find how long will it take for the… 2018 · 4 marks · Short answer
- Solve: $\frac{dy}{dx} = 1 - xy + y - x$ 2017 · 3 marks · Short answer
- Solve: $(x^2 - yx^2) \, dy + (y^2 + xy^2) \, dx = 0$ 2017 · 5 marks · Short answer
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