`(x^2+1)dy/dx+2xy=sqrt(x^2+4)` Obtain the general solution.

Consider the differential equation xdy/dx+2y=x^2 , x!=0 Obtain its general solution.

Consider the DE xdy-ydx=sqrt(x^2+y^2)dx Find the general solution.

(x^2+1)dy/dx+2xy=sqrt(x^2+4) Find its integrating factor.

Consider dy/dx=-(2xy)/(x^2+1) Find the general solution of the differential equation.

Express the differential equation (x^2+1)dy/dx+2xy=sqrt(x^2+4) in the form dy/dx+P(x)y=q(x) .

Prove that x^2 - y^2 = c(x^2 + y^2)^2 is the general solution of the differential equation (x^3 - 3xy^2) dx = (y^3 - 3x^2y) dy , Where c is a parameter.

Solve : (1+x^2)dy/dx+2xy-4x^2=0 .

Find the general solution of (dy)/(dx)=sin ^-1 x

Consider the differential equation x(d^2y)/dx^2+2dy/dx-xy+x^2-2=0 .Show that xy=ae^x+be^-x+x^2 is a solution of the given equation.

If xy = A sin x + B cos x is the solution of the differential equation x (d^2 y)/( dx^2) - 5a (dy)/( dx) + xy = 0 , then the value of a is