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11)Solve the PDE (x+y

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?


6)If L{f(t)}= e^{-2s}+4/s(2s

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


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