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`]]
\[ \boxed {\left (x +y\right ) y^{\prime }-y+x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve((y(x)+x)*diff(y(x),x)=(y(x)-x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 34
DSolve[(y[x]+x)*y'[x]==(y[x]-x),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {y(x)}{x}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]