Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
$$\frac{\mathrm dy}{\mathrm dx} = e^{yx}+\frac yx$$
I'm trying to solve the differential equation. Here is part of my attempt:
I know that i have to integrate both sides of the equation but when I try to integrate my answer doesn´t match with the book´s answer.
Given the fact that the book answer you cited is $y(x)=-x~\ln\ln\dfrac Cx~,~$ it follows that you've
misspelled the original equation, meaning that the question is actually supposed to read $y'(x)=$
$=\exp\bigg(\dfrac yx\bigg)+\dfrac yx~,~$ which begs for a substitution of the form $u(x)=\dfrac{y(x)}x~,~$ yielding $(x\cdot u)~'$
$=e^u+u.~$ But $(x\cdot u)~'=x\cdot u'+u\iff x~\dfrac{du}{dx}=e^u\iff\dfrac{dx}x=\dfrac{du}{e^u}~.$ I believe you can
take it from here.
$$and use alignment like this:$$\begin{align*} a & = b \\ \Rightarrow a + c & = b + c \end{align*}$$$$\begin{align*} a & = b \\ \Rightarrow a + c & = b + c \end{align*}$$ $\endgroup$