Internal problem ID [7792]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 212.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime } y+x +f \left (x^{2}+y^{2}\right ) g \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 30
dsolve(y(x)*diff(y(x),x)+f(x^2+y(x)^2)*g(x)+x=0,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}}{f \left (\textit {\_a}^{2}+x^{2}\right )}d \textit {\_a} +\int g \relax (x )d x -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 95
DSolve[y[x]*y'[x]+f[x^2+y[x]^2]*g[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{f\left (x^2+K[2]^2\right )}-\int _1^x-\frac {2 K[1] K[2] f'\left (K[1]^2+K[2]^2\right )}{f\left (K[1]^2+K[2]^2\right )^2}dK[1]\right )dK[2]+\int _1^x\left (g(K[1])+\frac {K[1]}{f\left (K[1]^2+y(x)^2\right )}\right )dK[1]=c_1,y(x)\right ] \]