Use the Mathematica software to find the solutio

3. Consider the Euler's differential equation: 3:23;\" 5my' + 93; = 3:4 + 22:3 1113:. (a) Find the general solution of this equation by using DSolve command. (b) Use DSoIVe command to nd the particular solutions of this equation that satises the initial conditions 9(1) = aay'(1)= 0-1- (0) Plot four solutions obtained in (b) by taking values for a = 0.1, 0.2, 0.5, 1 on the interval [0, 2] on the same coordinate system. 2. Consider the linear differential equation: y\" + 43/ + 13y = e23 sin(3:1:) + x4 + 51:6" cos(a:). (a) Find the general solution of this equation by using DSolve command. (b) Use DSolve command to nd the particular solutions of this equation that satises the initial conditions y(0) = .01,y'(0) = .02 and y(0) = 0,y'(0) = .01. (0) Plot the obtained solutions on the interval [0, 1] on the same coordinate system