Internal problem ID [8032]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 452.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {\left (2 x^{2}+1\right ) \left (y^{\prime }\right )^{2}+\left (y^{2}+2 y x +x^{2}+2\right ) y^{\prime }+2 y^{2}+1=0} \end {gather*}
✗ Solution by Maple
dsolve((2*x^2+1)*diff(y(x),x)^2+(y(x)^2+2*x*y(x)+x^2+2)*diff(y(x),x)+2*y(x)^2+1 = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 49
DSolve[1 + 2*y[x]^2 + (2 + x^2 + 2*x*y[x] + y[x]^2)*y'[x] + (1 + 2*x^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-c_1 x+1+c_1{}^2}{x+c_1} \\ y(x)\to -\frac {i}{\sqrt {2}} \\ y(x)\to \frac {i}{\sqrt {2}} \\ \end{align*}