List of top Mathematics Questions on General and Particular Solutions of a Differential Equation

The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :

The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

The integral $\int \frac{xdx}{2-x^{2}+\sqrt{2-x^{2}}}$ equals

The integral of $\frac{x^{2}-x}{x^{3}-x^{2}+x-1}$ w.r.t. x is

The number of solutions of the equation $ \sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x $ in $ \left[ 0,\frac{\pi }{2} \right] $ is

The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is

The differential equation of the family of curves $y = e^{2x} (a \,\cos\, x + b \,\sin\, x)$, where $a$ and $b$ are arbitrary constants, is given by

The number of solutions for the equation $Sin\, 2x + Cos \; 4x = 2$ is

Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

The differential equation of the system of all circles of radius $r$ in the $xy$ plane is

The differential equation whose general solution is $Ax^2 + By^2 = 1$, where $A$ and $B$ are arbitrary constants is of ?

The solutions of the equation $\begin{vmatrix} {x}&{2} &{-1}\\ {2}&{5}& {x} \\ {-1}&{z}&{x}\\ \end{vmatrix} =0$ are

Given function $f(x)=\left(\frac{e^{2 x}-1}{e^{2 x}+1}\right)$ is.

If f(x) is differentiable and $\int_0^{t^2}x f(x) dx =\frac{2}{5}t^5,$ then $f\bigg(\frac{4}{25}\bigg)$ equals

Let T > 0 be a fixed real number. Suppose, f is a continuous function such that for all $x \in R. f(x+T)=f(x). \, If \, I = \int_0^T f(x)dx$ then the value of $\int_3^{3+3T} f(2x)dx$

Let f(x) =$\int_1^x \sqrt{2-t^2}dt $ Then, the real roots of the equation $x^2-f'(x)=0$ are

If |x + 1||x + 3| – 4|x + 2| + 5 = 0, then sum of squares of solutions is

If $ {{x}^{y}}.{{y}^{x}}=16, $ then $ \frac{dy}{dx} $ at (2, 2) is

The integral $\int^{\pi/2}_{0}\left|sin\,x-cos\,x\right|dx$ is equal to :

The differential equation of all parabolas whose axis of symmetry is along axis of $x$-axis is of order

The differential equation of $y = Ae^{2x} + Be^{-2x} $ is :

Solution of the differential equation $\frac{x+\frac{x^{3}}{3!}+\frac{x^{5}}{5!}+\ldots}{1+\frac{x^{2}}{2!}+\frac{x^{4}}{4!}+\ldots}=\frac{dx-dy}{dx+dy}$ is

Solution of $|x^2 - 10| \le 6$ is

Solution of $\frac{dy}{dx}-y=1$, $y\left(0\right)=1$ is given by