Use the Laplace transform to solve the following initial value problem: y ′′
−10y ′
+9y=5t,y(0)=−1,y ′
(0)=2 [8 marks ] b) Solve the following initial value problem using a Laplace transform method. y ′′
−6y ′
+5y=3e 2t
,y(0)=2,y ′
(0)=3 [12 marks ] (c) Use the Laplace transform to solve the given system of differential equations: 2 dt
dx
​ + dt
dy
​ =5e t
dt
dy
​ −3 dt
dx
​ =5
​ Given that when t=0,x=0 and y=0.