Internal problem ID [8772]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 436.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} \left (-x^{2}+1\right )=x^{4}} \]
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 59
dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+y(x)^2*(-x^2+1)-x^4 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -i x y \left (x \right ) = i x y \left (x \right ) = -\frac {x \left (\frac {{\mathrm e}^{2 x}}{c_{1}^{2}}-1\right ) {\mathrm e}^{-x} c_{1}}{2} y \left (x \right ) = \frac {x \left ({\mathrm e}^{2 x} c_{1}^{2}-1\right ) {\mathrm e}^{-x}}{2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 60
DSolve[-x^4 + (1 - x^2)*y[x]^2 - 2*x*y[x]*y'[x] + x^2*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x e^{-x-c_1} \left (-1+e^{2 (x+c_1)}\right ) y(x)\to \frac {1}{2} \left (x e^{-x+c_1}-x e^{x-c_1}\right ) \end{align*}