the last integral does not integrate :
$\displaystyle xy' - y=ln(y); x=(ln(y) + y)/y'; y' = p; x=(ln(y) + y)/p; $
$\displaystyle dx=-1/p^2 (ln(y) + y)dp + (1/yp + 1/p)dy; $
$\displaystyle (ln(y)/p^2 + y/p^2)dp=dy/yp; dp/p = dy/(yln(y)+y^2)$
the last integral does not integrate :
$\displaystyle xy' - y=ln(y); x=(ln(y) + y)/y'; y' = p; x=(ln(y) + y)/p; $
$\displaystyle dx=-1/p^2 (ln(y) + y)dp + (1/yp + 1/p)dy; $
$\displaystyle (ln(y)/p^2 + y/p^2)dp=dy/yp; dp/p = dy/(yln(y)+y^2)$
The solution involves an integral that cannot be found using a finite number of elementary functions: integrate 1/(Log[y] + y) - Wolfram|Alpha
Where has the DE come from?
this DE was given to me by university tutor. and yes, i know that function doesn't integrate in elementary functions, but i thought that i am doing something wrong. by the way i have plenty DEs that i can't solve duo to integration for example in attachment. i think that i'm just doing something wrong. can someone help me.