Internal problem ID [7945]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 366.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve(f(x^2+a*y(x)^2)*(a*y(x)*diff(y(x),x)+x)-y(x)-x*diff(y(x),x) = 0,y(x), singsol=all)
\[ -\frac {a y \left (x \right )^{2} x}{\sqrt {a^{2} y \left (x \right )^{2}}}-\left (\int _{}^{-\frac {a y \left (x \right )^{2}}{2}-\frac {x^{2}}{2}}f \left (-2 \textit {\_a} \right )d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 91
DSolve[-y[x] - x*y'[x] + f[x^2 + a*y[x]^2]*(x + a*y[x]*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\left (x-a f\left (x^2+a K[2]^2\right ) K[2]-\int _1^x\left (1-2 a K[1] K[2] f'\left (K[1]^2+a K[2]^2\right )\right )dK[1]\right )dK[2]+\int _1^x\left (y(x)-f\left (K[1]^2+a y(x)^2\right ) K[1]\right )dK[1]=c_1,y(x)\right ] \]