Internal problem ID [4135]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 899.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+\left (-x^{2}+1\right ) y^{2}=x^{4}} \]
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 58
dsolve(x^2*diff(y(x),x)^2-2*x*diff(y(x),x)*y(x)-x^4+(-x^2+1)*y(x)^2 = 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 ({\mathrm e}^{x}-c_{1}^{2} {\mathrm e}^{-x}\right )}{2 c_{1}} \\ y \left (x \right ) &= \frac {x \left (c_{1}^{2} {\mathrm e}^{x}-{\mathrm e}^{-x}\right )}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 60
DSolve[x^2 (y'[x])^2-2 x y[x] y'[x]-x^4+(1-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*}