List of top Mathematics Questions on Differential equations asked in TS EAMCET

Differential equation for family \(y=ae^{2x}+bx^2\) is

If \(y=f(x)\) satisfies \[ \tan x \frac{dy}{dx}+(1+\tan^2 x)y=\tan x(1+\tan^2 x)^2 \] and passes through \(\left(\frac{\pi}{4},\frac{3}{4}\right)\), find \(f\left(\frac{\pi}{3}\right)\)

If \[ \frac{dy}{dx} = (x^3-x) -(1-3x^2)\tan x +(x^3-x)\tan^2x \] and \[ y(1)=0, \] then \[ \frac{64}{\pi}y\!\left(\frac{\pi}{4}\right) = ? \]

If \[ \frac{dy}{dx} - \frac{2x}{x^2+b}y = -2x(x^2+b), \] with \[ y(0)=12,\qquad y(1)=10, \] then the sum of all possible values of \(b\) is:

The solution of the differential equation \[ \frac{dy}{dx} = \frac{3^{x+y}-2\cdot3^x} {3^{x+y}-2\cdot3^y} \] when \[ y(1)=2 \] is:

The general solution of the differential equation \[ (2xy+y^2)\,dy=(x^2-y^2)\,dx \] is:

If the general solution of $(1+y^2)dx = (\tan^{-1}y - x)dy$ is $x = f(y)+ce^{-\tan^{-1}y}$, then $f(y)=$

The differential equation of the family of all circles of radius 'a' is

If the differential equation having $y = Ae^x + B\sin x$ as its general solution is $f(x)\frac{d^2y}{dx^2}+g(x)\frac{dy}{dx}+h(x)y=0$, then $f(x)+g(x)+h(x) =$

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is

The general solution of the differential equation $(x^3-y^3)dx = (x^2y-xy^2)dy$ is

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2x$ and eccentricity is $\sqrt{3}$ is