Chemical Engineering Answers

1)Eliminate the arbitrary function from z= xy+f(x²+y²) to obtain the partial differential equation.

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6)Solve ∂²z/∂x²-∂²z/∂y²=e^{x-2y}+ cos(2x+3y).

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5) Find the particular integral of ∂²z/∂x²-3 ∂²z/∂x∂y+∂²z/∂y²= 2x sin y.

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6) Solve the initial value problem y''-4y=cos 3t ,y(0)=0,y'(0)=1

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5)Solve the integral equation f(t)=t+3 ∫0^t f(τ)dτ?

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4) Find the inverse Laplace transform of 5/(s-1)(s+4) without using partial fractions.

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3) Find the inverse Laplace transform of ln(s+3/s²+9).

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2) Find the Laplace transform of the periodic function f(t)=t ,0≤t≤2 and f(t+2)=f(t)?

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1)Find the Laplace transform of sinh t/t?

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6) Evaluate ∮c ze^{z)/(z-1)²(z²+4) dZ,Where C is |z-1|=1 by using Cauchy integral formula for derivatives.

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