Differential Equations Answers

SOLVE THE GIVEN DIFFERENTIAL EQUATION BY SEPARATION OF VARIABLES
DY/DX=Y-2/X-1
Y(2)=2

x^2(y-1)uxx-x(y^2-1)uxy+y(y-1)uyy+(xy)ux-uy =0
Reduce into canonical form and solve it

How to solve
Determine if the following W = (y+z)dx + (x+z)dy + (x+y)dz has a primitive.

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