Differential Equations Answers

Find the temperature in a bar of length l with both ends insulated and with initial temperature in the rod being sin πx/L.

Using the method of separation of variables, solve uxt = e^-1 cos x when u(x,0) =0, du/dt (0,t)= 0

Find the equation of the integral surface of the differential equation (x^2-yz)p+(y^2-zx)q= z^2-xy which passes through the line x =1, y =0.

Solve the differential equation (1) x^2p + y^2q = (x+y)z. (2) p^1/2 -q^1/2 +3x =0

Verify that the pfaffian differential equation yz dx+ (x^2y-zx) dy +(x^2z-xy) dz = 0 is integrable and hence find its integral.

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

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.

Write the ordinary differential equation ydx+(xy+x-3y)dy=0 in the linear form , and hence find its solution.

Solve dy/DX +xy= y^2e^x^2/2sin x

The pde uxx+ x^2 uxy -(x^2/2+1/4) uyy = 0 is hyperbolic in the entire xy-plane.true or false why?