Question

I need your help, please! I'm taking this course at my university, but I don't know what should i do about this differential equation: y'=(3*e^(x+y))/(x^2+2): I solved it online, but the solution has 'Ei(x)' (The exponential integral)!

Answer 1

Did you use variable separation? What is the form of the equation that needs the exponential integral?

Answer 2

\[\begin{align}y'&=\frac{3e^{x+y}}{x^2+2}\\\frac{\mathrm dy}{\mathrm dx}&=\frac{3e^xe^y}{x^2+2}\\\frac{\mathrm dy}{e^y}&=\frac{3e^x\mathrm dx}{x^2+2}\\\int e^{-y}\mathrm dy&=3\int\frac{e^x}{x^2+2}\mathrm dx\\&=\end{align}\]