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 $y^{\prime }{y}^{‴}=3{\left(y^{″}\right)}^2$

Which equation represents the consumption function?

In which year was the Permanent Settlement of Bengal introduced?

Which measure of GDP adjusts for price changes over time?

Which of the following is measured by nominal GDP?

What is the primary function of the General Ledger in a CAS?

Macroeconomics emerged as a distinct field of study during which event?

What was the primary demand of the Naga insurgents?

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 $y^{\text{'}\text{'}}+\left(2\tan 2x\right)y^{\prime }=$