SOLUTION: In this problem you will use variation of parameters to solve the nonhomogeneous equation t^(2)y′′+ty′−4y=3t^(3)+2t^(2) A. Plug y=tn into the associated homogeneous equa

Question 1184693: In this problem you will use variation of parameters to solve the nonhomogeneous equation t^(2)y′′+ty′−4y=3t^(3)+2t^(2)
A. Plug y=tn into the associated homogeneous equation (with "0" instead of "3t3+2t2") to get an equation with only t and n.
My answer n(n-1)t^n+nt^n-4t^n=0 , CORRECT
B. Solve the equation above for n (use t≠0 to cancel out the t).
You should get two values for n, which give two fundamental solutions of the form y=t^(n).
My answer y1= t^2 , y2= 1/t^2 , W(y1,y2)= -4/t , CORRECT
C. To use variation of parameters, the linear differential equation must be written in standard form y′′+py′+qy=g. What is the function g?
My answer g(t)= 3t+2 , CORRECT
D. Compute the following integrals.
∫y1g/W dt= -3/20t^5-1/8t^4 , CORRECT
∫y2g/W dt= -1/4(3t+2ln(t)) , CORRECT
E. Write the general solution. (Use c1 and c2 for c1 and c2).
y=c1t^2+c2/t^2-3/20t^7-1/8t^6-3/4*1/t+2/t^2ln(t) , WRONG
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The particular solution is given by

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