The discussion revolves around checking the solution of a differential equation, specifically xy' - 2y = x^3e^x, with the proposed solution y = x^2e^x. Participants are exploring the process of verifying this solution through substitution.
The conversation indicates a shift in understanding, with some participants recognizing the importance of substitution over solving for x. Guidance has been offered regarding the approach to take, but there is no explicit consensus on the best method yet.
There appears to be a misunderstanding about the steps involved in verifying the solution, with some participants questioning the need to solve for x instead of simply substituting the solution into the equation.
Why solve for x ?asadpasat said:Homework Statement
The differential equation is xy'-2y= x3ex
Check the solution y=x2 ex
Homework Equations
Just plug in
The Attempt at a Solution
y' = x2ex + 2xex
Having problem solving for x.
Chestermiller said:Why are you trying to solve for x? Just substitute your solution for y into the differential equation.
Chet