List of top Mathematics Questions on Differential equations asked in WBJEE

A missile is fired from the ground level rises x meters vertically upwards in t sec, where \(x=100t-\frac{25}{2}t^2\). the maximum height reached is

f(x) is differentiable function and given f'(2)=6, f'(1)=4, then \(\lim_{h\rightarrow0}\frac{f(2+2h+h^2)-f(2)}{f(1+h-h^2)-f(1)}\)

Let f be a non-negative function defined on [\(0,\frac{\pi}{2}\)]. If \(\int_{0}^{x}(f'(t)-sin\,2t)dt=\int_{0}^{x}f(t)tan\,t\,dt\). \(f(0)=1\), then \(\int_{0}^{\frac{\pi}{2}}f(x)dx\) is

If y=\(\frac{x}{log_e|cx|}\) is the solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}+\phi(\frac{x}{y})\), then \(\phi (\frac{x}{y})\) is given by 

The family of curves y=e^{asin x}, where a is an arbitrary constant, is represented by the differential equation

General solution of $\left(x+y\right)^{2} \frac{dy}{dx} = a^{2}, a \ne 0$ is (c is an arbitrary constant)

The integrating factor of the first order differential equation $x^{2}\left(x^{2}-1\right) \frac{dy}{dx}+x\left(x^{2}+1\right)y=x^{2}-1$ is

General solution of $y \frac{dy}{dx}+by^{2}=a\,cos\,x, 0 < x< 1$ is

The integrating factor of the differential equation $\frac{d y}{d x}+\left(3 x^{2} \tan ^{-1} y-x^{3}\right)\left(1+y^{2}\right)=0$is

If $\sqrt{y}=cos^{-1}x,$ then it satisfies the differential equation $\left(1-x^{2}\right)-x \frac{dy}{dx}=c,$ where $c$ is equal to

The solution of $25\frac{d^{2}y}{dx^{2}}-10 \frac{dy}{dx}+y=0, \, y\left(0\right) =1, \, y\left(1\right)=2e^{\frac{1}{5}} $ is

Solution of the differential equation $xdy - ydx = 0$ represents a

The general solution of the different equation $100\frac{d^{2}y}{dx^{2}}-20 \frac{dy}{dx}+y = 0 $ is

The degree of the differential equation $x = 1+\left(\frac{dy}{dx}\right)+\frac{1}{2!}\left(\frac{dy}{dx}\right)^{2}+\frac{1}{3!}\left(\frac{dy}{dx}\right)^{3} + .........$

If $y'' - 3y' + 2y = 0$ where $y(0) = 1$, $y'(0) = 0$, then the value of $y$ at $x \,= log_e \,2$ is

The equation of one of the curves whose slope at any point is equal to $y + 2x$ is

The slope at any point of a curve $y = f(x )$ is given by $\frac{d y}{d x}=3x^{2}$ and it passes through $(-1 ,1 )$ The equation of the curve is

The order and degree of the following differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/2} = \frac{d^{3}y}{dx^{3}}$ are respectively

The differential equation of the family of circles passing through the fixed points $(a, 0)$ and $(-a, 0)$ is

The minimum value of $f(x)={\sin }^{4}x+{\cos }^{4}x,0\le x\le \frac{\pi }{2}$

The probability that in a family of 5 members, exactly 2 members have birthdays on Sunday, is

If A1, A2; G1, G2; and H1, H2 are two AMs, GMs and HMs between two quantities, then the value of $\frac{G_1{G}_2}{H_1{H}_2}$ is

Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax² + bx + c = 0 

For the real parameter $t$, the locus of the complex number $z=(1-t^2)+i\sqrt{1+t^2}$

The coefficient of $x_n$ in the expansion of $\frac{e^{7x}+e^x}{e^{3x}}$ is