Math Answers

Show that the wave equation a^2uxx = utt can be reduced to the form u xi×ita by the change of variable xi=x-at, ita = x+at.

Solve the following differential equations (i) [D^3-DD'^2-D^2+DD']z (ii) [D^4-D'^4-2D^2D'^2]z =0 (iii) [D^2-2DD'+D'^2]z =12xy.

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

Show that 2z =(ax+y)^2 + B , where a, b are arbitrary constants is a complete integral of px+qy-q^2 = 0

Solve the following equation by Jacobi’s method x^2 du/dx -(du/dx)^2 - (du/dz)^2 =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.