CooperSection 13.2 #3

Find the general solution of the following equations by integrating.(Note: Please useA for the first constant of integration,B for the second, andCfor the third.)

a. The differential equation((d^3)x)/(dt^3)=4t^3+thas general solutionx= __________________________

a-1. The differential equation 2y'=3t+2 has general solutiony= __________________________

b. Find the solution of the differential equation y'=(4t+1)^2 satisfying the initial condition y(0)=2. Solution:y= __________________________

c. Find the solution of y'=4y, which has initial condition y(0)=2. Solution:y(t)= __________________

d. Find the general solution of the equation y''=e^(3t). Please useA for the first constant of integration andB for the second. Solution:= ____________________