Differential Equations: JEE Main Mathematics Previous Year Questions

326 previous year questions from Differential Equations. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.Let $y=y\left(x\right)$ be the solution of the differential equation $2\text{co}sx\frac{dy}{dx}=\text{si}n2x-4y\text{sin}x\text{,}x$…
2. 2.The general solution of the differential equation $\sqrt{1-x^2{y}^2}\cdot \text{dx}=y\cdot \text{dx}+x\cdot \text{dy}$ is
3. 3.The general solution of the differential equation $\sqrt{1+x^2+y^2+x^2{y}^2}+\text{xy}\frac{\text{dy}}{\text{dx}}=0$ is : (where$C$ is a constant of integ…
4. 4.The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}+\frac{y}{x}=x^2$ is
5. 5.The general solution of $x\frac{\text{dy}}{\text{dx}}=y-x\text{tan}\text{⁡}\left(\frac{y}{x}\right)$ is
6. 6.$a\text{,}b\text{,}c\text{,}d$ are arbitrary constants. Then the corresponding differential equation to $y=a{e}^x+b{e}^{-x}+\text{ccos}\text{⁡}x+\text{dsin}\text{⁡}x$…
7. 7.A gardener is digging a plot of land. As he gets tired, he works more slowly. After ' $t$ ' minutes he is digging at a rate of $\frac{2}{\sqrt{t}}$ square metres per mi…
8. 8.The differential equation satisfied by the system of parabolas$y^2=4a(x+a)$ is:
9. 9.If the solution $y\text{(}x\text{)}$ of the given differential equation $(e^y+1)\text{cos}\text{⁡}xdx+e^y\text{sin}\text{⁡}xdy=0$ passes through t…
10. 10.The order of the differential equation of all circles whose radius is 4 , is
11. 11.The general solution of the differential equation $(1+y^2)$ $\text{dx}=({\text{tan}}^{-1}\text{⁡}y-x)\text{dy}$ is
12. 12.The sum of the degree and order of the differential equation ${(1+y_1^2)}^{2/3}=y_2$ is
13. 13.Let $y=y\text{(}x\text{)}$ be the solution of the differential equation…
14. 14.Find the sum of the order and degree of the differential equation $y=x{\left(\frac{\text{dy}}{\text{dx}}\right)}^3+\frac{d^{2}y}{d{x}^2}$
15. 15.If the length of the sub tangent at any point $p\text{(}x\text{,}y\text{)}$ on a curve $f\text{(}x\text{,}y\text{)}=0$ is $x+7y^2$, then…
16. 16.The family of curves represented by the general solution of $y^{\text{’}}=\frac{y}{2x}$ contains
17. 17.The solution of $\frac{d^{2}y}{d{x}^2}=0$ represents
18. 18.The general solution of the differential equation of all circles having centre at $A\text{(}-1\text{,}2\text{)}$ is
19. 19.The solution curve, of the differential equation $2y\frac{dy}{dx}+3=5\frac{dy}{dx}$, passing through the point $\text{(}0\text{,}1\text{)}$ is a conic, wh…
20. 20.Let $y=y\left(x\right)$ be the solution of the differential equation $(x^2-3y^2)\text{dx}+3\text{xy}\text{dy}=0$, $y\left(1\right)=1$. The…
21. 21.The solution of the differential equation $2x\left(\frac{\text{dy}}{\text{dx}}\right)-y=4$ represents a family of
22. 22.If $a$ and $b$ are respectively the order and degree of a differential equation…
23. 23.The degree of the differential equation ${(1+{\left(\frac{\text{dy}}{\text{dx}}\right)}^2)}^2=\frac{d^{2}y}{d{x}^2}$ is
24. 24.The solution of $(1+y^2)\text{dx}-\text{xydy}=0\text{,}y\text{(}1\text{)}=0$ represents a conic. Its eccentricity is
25. 25.The curve passing through the point $\text{(}1\text{,}2\text{)}$ given that the slope of the tangent at any point $\text{(}x\text{,}y\text{)}$ is $2x/y$ represents