Internal problem ID [8123]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 543.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {x y^{2} \left (y^{\prime }\right )^{3}-y^{3} \left (y^{\prime }\right )^{2}+x \left (x^{2}+1\right ) y^{\prime }-y x^{2}=0} \end {gather*}
✗ Solution by Maple
dsolve(x*y(x)^2*diff(y(x),x)^3-y(x)^3*diff(y(x),x)^2+x*(x^2+1)*diff(y(x),x)-x^2*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.464 (sec). Leaf size: 399
DSolve[-(x^2*y[x]) + x*(1 + x^2)*y'[x] - y[x]^3*y'[x]^2 + x*y[x]^2*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )} \\ y(x)\to \sqrt {c_1 \left (x^2+\frac {1}{1+c_1{}^2}\right )} \\ y(x)\to -\frac {\sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to -\frac {i \sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to \frac {\sqrt [4]{-8 x^4+20 x^2-\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to -\frac {\sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to -\frac {i \sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ y(x)\to \frac {\sqrt [4]{-8 x^4+20 x^2+\sqrt {-\left (8 x^2-1\right )^3}+1}}{2^{3/4}} \\ \end{align*}