10)Find the complete integral of the PDE yq+3xp=2(z-y²p²).
Explain the problem with step by step process?
9) Eliminate the arbitrary constants a and b from the equation (x-a)²+(y-b)²+z²=2019 to obtain the partial differential equation.
Explain the problem with step by step process?
8)Solve (D²+3DD'+2D'^2)z=x cos y+e^x+y, Where D=∂\∂x and D'=∂\∂y.
Explain the problem with step by step process?
7)Find the integral surface of x(y²+z)p-y(x²+z)q=(x²-y²)z through the curve x+y=0,z=1.
Explain the problem with step by step process?
5)Solve ∫0^t y''(τ)y'(t-τ)dτ=y(t),y(0)=y'(0)=20
4)Define Laplace transform and find Laplace transform of the periodic function f(t) =t,0≤t≤2 and f(t+2)=f(t)
3) Find the Laplace transform of 1-e^{-2t}/t
2)Solve y" + 3y' +2y= t²δ(t-2),y(0)=0,y'(0) =-2