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Yukti Vault

Calculus

Differential Equation: JEE Main & Advanced PYQs

313 previous year questions on Differential Equation from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 301-313 of 313

  1. Let $y=f(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+\dfrac{xy}{x^{2}-1}=\dfrac{x^{6}+4x}{\sqrt{1-x^{2}}}$, $-1<x<1$ such that $f(0)=0$. If …
  2. Let a curve $y=f(x)$ pass through the points $(0,5)$ and $(\log_e2,k)$. If the curve satisfies the differential equation $2(3+y)e^{2x}dx-\left(7+e^{2x}\right)dy=0$, then …
  3. Let $y=y(x)$ be the solution of the differential equation $2\cos x\dfrac{dy}{dx}=\sin2x-4y\sin x$, $x\in\left(0,\dfrac{\pi}{2}\right)$. If …
  4. Let $f:(0,\infty)\to\mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^{2}f'(x)=2xf(x)+3$, with $f(1)=4$. Then …
  5. If $y=y(x)$ is the solution of the differential equation …
  6. A function $y=f(x)$ has a second order derivative $f''(x)=6(x-1)$. If its graph passes through the point $(2,1)$ and at that point the tangent to the graph is $y=3x-5$ …
  7. The differential equation for the family of circles $x^{2}+y^{2}-2ay=0$, where $a$ is an arbitrary constant, is :
  8. The differential equation of all circles passing through the origin and having their centres on the $x$-axis is :
  9. The differential equation which represents the family of curves $y=c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants, is
  10. The differential equation of the family of circles with fixed radius $5$ units and centre on the line $y=2$ is :
  11. Let for some function $y=f(x)$, $\int_{0}^{x}tf(t)\,dt=x^{2}f(x)$, $x>0$ and $f(2)=3$. Then $f(6)$ is equal to
  12. Let a curve $y=y(x)$ be given by the solution of the differential equation $\cos\left(\dfrac{1}{2}\cos^{-1}\left(e^{-x}\right)\right)dx=\sqrt{e^{2x}-1}\,dy$. If it …
  13. Let $y=y(x)$ satisfy the equation $\dfrac{dy}{dx}-|A|=0$, for all $x>0$, where $A=\begin{bmatrix}y&\sin x&1\\0&-1&1\\2&0&\dfrac{1}{x}\end{bmatrix}$. If $y(\pi)=\pi+2$ …

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