Math Answers

Solve the following DEs (I) (dy/dx-1)^2(d^2y/dx^2 +1)^2 y = sin^2(x/2)+x. (2) 2x^2y(d^2y/dx^2)+4y^2= x^2(dy/dx)^2 + 2xy(dy/dx).

Solve : x×dy/dx+y lny = xye^x.

Find the charge on the capacitor in an RLC circuit at t= 0.01sec. when L= 0.05 Henry, R= 2 ohms, C= 0.01 Farad. E(t) =0, q(0)= 5 Columbus and I(0)=0.

Solve : d^2y/dx^2 -2tanx dy/dx +5y = e^x. sec x

Solve the following IVP d^2y/dx^2+ dy/dx -2y = -6sin2x -18cos2x, y(0) =2, y'(0)= 2

Solve the equation x^2×d^2y/dx^2+x×dy/dx +y = x^m , for all positive integer values of m.

Find the integrating factor of the differential equation (6xy-3y^2+2y)dx +2(x-y)dy=0 and hence solve it.

Solve the following equation by changing the independent variable (1+x^2)^2y"+2x(1+x^2)y'+4y=0.

Solve, using the method of variation of parameters d^2y/dx^2-y=2/1+e^x.

Given that y1(x)= x^-1is one solution of the differential equation 2x^2y"+3xy'-y=0,x>0, find a second linearly independent solution of the equation.