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(Solved): A first order linear equation in the form y^(')+p(x)y=f(x) can be solved by finding an integrating f ...
A first order linear equation in the form y^(')+p(x)y=f(x) can be solved by finding an integrating factor \mu (x)=exp(\int p(x)dx)
(1) Given the equation xy^(')+(1+2x)y=8e^(-2x) find \mu (x)=
(2) Then find an explicit general solution with arbitrary constant C.
y=?
(3) Then solve the initial value problem with y(1)=e^(-2)
y=?