Linear Differential Equation - Initial Value Problem

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SUMMARY

The discussion revolves around solving a linear differential equation with an initial value problem. The user successfully calculated the integrating factor μ(x) = e^x - x² and applied it to the equation. The confusion arose when the user noticed a discrepancy in the resulting equation, which was clarified upon realizing that the left side of the equation represented the derivative of e^x - x² ⋅ y. This insight allowed for simplification, resolving the initial misunderstanding.

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thaalescosta
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Hello, I'm struggling with a simple problem here.

It asks me to solve the following initial value problem:
fSfRWNn.png


So far I've calculated the integration factor μ(x) = ex-x2 and I multiplied both sides of the equation by it and got this:
http://www4c.wolframalpha.com/Calculate/MSP/MSP36171f59839bdf0g6cbd000044defig6e40h0ei0?MSPStoreType=image/gif&s=64&w=256.&h=47.

The problem I'm having is that the equation I got is different than the equation in the first line of the solution:
2zu70dx.png


I don't understand how the ex-x2⋅(1 - 2x)⋅y disappearedEDIT: Actually, nevermind. My brain was too lazy to realize that the left part of the equation is equal to the derivative of ex-x2⋅y so I could just simplify it
​
 
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Well done.
 

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