General and Particular Solutions of a Differential Equation

If $f\left(x\right)f^{\text{'}}\left(-x\right)=f\left(-x\right)f^{\text{'}}\left(x\right)$, then the value of $f\left(x\right)f\left(-x\right)$ for all $x$ is given $f\left(0\right)=3$

If $\frac{dy}{dx}=y+3$ and $y\left(0\right)=2,$ then $y\left(\ln 2\right)$ is equal to

Solution of differential equation $\left(x^{2}y-2x{y}^2\right)dx-\left(x^3-3x^{2}y\right)dy=0$ is

Solve :

$\left(1+x^2\right)\frac{dy}{dx}+y=e^{{\tan }^{-1}}x$.

The differential equation whose general solution is $y=\log x+c$ is

The general solution of the differential equation $\frac{dy}{dx}=\frac{2y}{x}$ is,

Solution of equation $x\log x\frac{dy}{dx}+y=2\log x$

General solution of equation $y(1+x)dx+x(1+y)dy=0$ is

Find the general solution of the differential equation $$$\frac{dy}{dx}+\left(\sec x\right)y=\tan x$, $\left(0\le x<\frac{\pi }{2}\right)$

The general solution of the differential equation $\frac{dy}{dx}=\frac{2x-3y+4}{3x+2y-7}$ is

Which of the following is solution of the differential equation $y^{\prime }{y}^{‴}=3{\left(y^{″}\right)}^2$

A curve is such that the $x$-intercept of the tangent drawn to it at the point $P\left(x,\mathrm{}y\right)$ is reciprocal of the abscissa of $P.$ Then, the equation of the curve is (where, $c$ is the constant of integration and $x>1$)

If $y=a\cos \left(\sin 2x\right)+b\sin \left(\sin 2x\right),$ then $y^{\text{'}\text{'}}+\left(2\tan 2x\right)y^{\prime }=$

The solution of the differential equation $\left(2x-4y+3\right)\frac{dy}{dx}+\left(x-2y+1\right)=0$ is

The solution of the equation $\frac{d^{2}y}{d{x}^2}=e^{-2x}$ is

The solution of the equation $\left(x{y}^4+y\right)dx-xdy=0$ is

The general solution of $\mathrm{y}.\mathrm{ }\frac{{\mathrm{d}}^2\mathrm{y}}{\mathrm{d}{\mathrm{x}}^2}={\left(\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}\right)}^2$ is - {Where C_1,C₂ are arbitrary constant}

The solution of $\frac{dy}{dx}+y\tan x=\sec x$ is

The general solution of the differential equation $\frac{dy}{dx}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$ is (where $c$ is an arbitrary constant)

The differential equation $\frac{d^{2}y}{d{x}^2}=2$ represents