Solve the following differential equation using reduction of order. t^2 y’’ + 9ty’ -3 = 0 Also, solve the initial value problem subject to the initial conditions y(1) = 4 and y’(1) = 3/8 , t > 0

Question.

Solve the following differential equation using reduction of order.

t²y’’ + 9ty’ -3 = 0

Also, solve the initial value problem subject to the initial conditions y(1) = 4 and y’(1) = 3/8 , t > 0

Solution: