Differential Equations Answers

y"+xy'+(x^2 +2)y=0

(D^3 - 27) = e^3x + e^-3x

(2x+3y)dx-4(x+1)dy=0

Solve Laplace’s equation for u(x, y):

d2y/dx2 + d2u/dy2 = 0
0 < x < 2 , 0 < y < 1
u(x, 0) = sin πx , u(x, 1) = x/2
u(0, y) = sin πy , u(2, y) = y

Apply Charpit's method to solve the equation z-px-qy=p^2+q^2

Apply the method of variation of parameters to solve the following differential equation
d^2y/dx^2+ x^2/y=secnx , where n is a constant

Solve the differential equation
xdx+ydy= a^2(xdy-ydx)/x^2+ y^2

Solve the simultaneous equation
dx/(x-y)y^2 = dy/-(x-y)x^2 = dz/z(x^2+y^2)

Solve
x^2y''- 2xy'+2(1+x^2)y=0 , x>0

Write the equation ydx+ (x-y+x-2y)=0 in the linear form and hence find its solution.