3.7 problem 4(d)

Internal problem ID [2597]

Book: Differential equations with applications and historial notes, George F. Simmons, 1971
Section: Chapter 2, section 10, page 47
Problem number: 4(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {\left (x +y\right ) y^{\prime }-y+x=0} \end {gather*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 24

dsolve((y(x)+x)*diff(y(x),x)=(y(x)-x),y(x), singsol=all)
 

\[ y \relax (x ) = \tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]

Solution by Mathematica

Time used: 0.04 (sec). Leaf size: 34

DSolve[(y[x]+x)*y'[x]==(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\text {ArcTan}\left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]