3. Problem: Solve y'-2xy=e. Fictional Student Work: First order linear equation so y 1 µ(x) √ √µ(x)ƒ (x)dx. μ(x)=√ Sp(x)dx [2x dx and p(x)=2x so uµ(x) = e˜¨ = √ e¨ª³ · e* dx = y = e¯*ª √ e²² dx. Prompts: a) While sometimes we do have to leave our answers in integral form, the student only had to do so here because of an earlier error. What error was made? b) Give a suggestion for how the student could avoid this same error in the future. (Suggestions must be specific to the problem and not just a restatement of what the error was.) c) The student used the formula y = √μ(x)f(x)dx to find the solution, but this is not the µ(x) only valid method. List at least one other method that can be used to solve the differential equation. d) Rework the problem correctly using either the same method as the student or one of the methods you listed above.

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