Internal problem ID [12158]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 80.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact, _rational]
\[ \boxed {y y^{\prime }-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}=-x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 29
dsolve(x+y(x)*diff(y(x),x)= y(x)/(x^2+y(x)^2)- x/(x^2+y(x)^2)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-\tan \left (\textit {\_Z} \right )^{2} x^{2}-x^{2}+2 c_{1} -2 \textit {\_Z} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 31
DSolve[x+y[x]*y'[x]== y[x]/(x^2+y[x]^2)- x/(x^2+y[x]^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\arctan \left (\frac {x}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]