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.

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.

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.

Let y(t) be the solution of the initial value problem (d ^ 2 * y)/(d * t ^ 2) + a * d/dt (y) + by = f(t) a > 0 y(0) = 0 b > 0 d/dt (y) * (0) = 0 obtained by the method of Laplace transform. Then a ne b, a ^ 2 - 4b = 0(A) y(t) = integrate tau * e ^ ((- a * tau)/2) * f(t - tau) dtau from 0 to t(B) y(t) = integrate e ^ ((- a * tau)/2) * f(t - tau) dtau from 0 to t(C)y(t) = integrate tau * e ^ ((- b * tau)/2) * f(t - tau) dtau from 0 to t(D)y(t) = integrate e ^ ((- b * tau)/2) * f(t - tau) dtau from 0 to t

Identify the type of the differential equation (as linear, homogeneous,exact, separable or Bernoulli) and solve the initial value problemdydt = 2 sin(t) − y, with y(π2)= 3

Determine the Laplace Transform of the functionf(t)=−9δ(t−10)