When solving first-order PDEs using Laplace transforms, what is typically done after applying the Laplace transform?a.Solve the resulting algebraic equationb.Apply the inverse Laplace transformc.Apply the convolution theoremd.Apply boundary conditions

Determine the Laplace transforms of the initial value problem (IVP)y′′−3y′+2y=4δ(t−3),y(0)=0,y′(0)=0𝑦″−3𝑦′+2𝑦=4𝛿(𝑡−3),𝑦(0)=0,𝑦′(0)=0and obtain an expression for Y(s)=L(y)(t)𝑌(𝑠)=𝐿(𝑦)(𝑡). Do not find the inverse Laplace transform of the resulting equation.

The ODE y"+siny=0 cannot be solved using Laplace transform because (i) The given ODE is nonlinear (ii) The ODE is homogeneous (iii) The initial conditions are not provided.

Write – Laplace equation

Determine the Laplace transforms of the initial value problem (IVP)y′′−y′−30y=9u(t−5),y(0)=0,y′(0)=0𝑦″−𝑦′−30𝑦=9𝑢(𝑡−5),𝑦(0)=0,𝑦′(0)=0and obtain an expression for Y(s)=L(y)(t)𝑌(𝑠)=𝐿(𝑦)(𝑡). Do not find the inverse Laplace transform of the resulting equation.

Determine the inverse Laplace Transform of the functionF(s)=−4e−10ss𝐹(𝑠)=−4e−10𝑠𝑠Note: You must use the notation u(t−c)𝑢(𝑡−𝑐) rather than uc(t)𝑢𝑐(𝑡) in order for your answer to be accepted by SOWISO.