Differential Equations Answers

Solve the system of ODE by using Laplace transform :

dx/dt+dy/dt+2x+2y=e^t ,x(0)=1,y(0)=0

Determine the integral surface of x(y^2-u)Ux-y(x^2-u)Uy=(x^2-y^2)U

With data x+y=0,U=1

Solve the differential equation

(1-x^2) d2y/dx2 -2x dy/dx + y =0

. Derive the differential equation for RLC circuits and find the charge on the capacitor in an RLC series where L = 2 Henry, R = 16 Ohms, C = 0.02 Farads and E(t) = 100V . Assume the initial charge as the capacitor is 0C and the initial current is 5A. What happened to the charge on the capacitor over time?

Solve the differential equation dx where d²x/dt² + (g/l)*x= (g/l)*L, 1, L are constants subject to the dx conditions, x = a , dx/dt = 0 at t = 0

Find a solution of the differential equation x²y" + 4xy - (x² − 2)y = 0 using Frobenius method.

(X2-X) y"-xy' + y=0

Solve using natanis method

(x-y)dx-xdy+zdz=0

Solve the following :-

a) Find the solution of the differential equation:

(ax + hy + g)dx + (hx + by + f )dy = 0

b) Use the method of undermined coefficients to find the general solution of the

differential equation:

d^3y/dx^3 + d^2y/dx^2 = 3e^x + 4x^2

c) Solve the differential equation:

dy/dx - (3/2x)y = 2x/y

d) Use the method of variation of parameters to solve the differential equation:

y''' + 3y' + 2y = 4e^x

e) Find the integral curve of the differential equations:

dx/( x^2 - y^2 - z^2 ) = dy/2xy = dz/2xz

f) Find a particular integral of differential equation:

(D^3 - D' ^3)z = x^3 × y^3