The forum discussion focuses on solving the second-order linear differential equation 4y'' - 4y' + y = 16e^(t/2). The correct solution is identified as 2t^2 e^(t/2). A key step in the solution process involves dividing the equation by the coefficient of y'', leading to the simplified form y'' - y' + (1/4)y = 4e^(t/2). The participants emphasize the importance of correctly applying the variation of parameters method, specifically using the equations v1 = -∫ y2g/w and v2 = ∫ y1g/w.
PREREQUISITESStudents studying differential equations, mathematics educators, and anyone seeking to improve their problem-solving skills in second-order linear equations.
hahaha158 said:Homework Statement
solve 4y''-4y'+y=16et/2
Homework Equations
v1= -∫ y2g/w
v2= ∫ y1g/w
The Attempt at a Solution
http://imgur.com/gxXlfdH
the correct answer is 2t^2 e^(t/2) instead of what i have though, i am not sure what i am doing wrong?