Internal problem ID [3702]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 978.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 107
dsolve(y(x)^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-x^2+2*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x \\ y \left (x \right ) = x \\ y \left (x \right ) = \sqrt {-2 \sqrt {2}\, x c_{1} -c_{1}^{2}-x^{2}} \\ y \left (x \right ) = \sqrt {2 \sqrt {2}\, x c_{1} -c_{1}^{2}-x^{2}} \\ y \left (x \right ) = -\sqrt {-2 \sqrt {2}\, x c_{1} -c_{1}^{2}-x^{2}} \\ y \left (x \right ) = -\sqrt {2 \sqrt {2}\, x c_{1} -c_{1}^{2}-x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.505 (sec). Leaf size: 169
DSolve[y[x]^2 (y'[x])^2-2 x y[x] y'[x]-x^2+2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-4 \sqrt {2} e^{c_1} x-4 e^{2 c_1}} \\ y(x)\to \sqrt {-x^2-4 \sqrt {2} e^{c_1} x-4 e^{2 c_1}} \\ y(x)\to -\sqrt {-x^2+4 \sqrt {2} e^{c_1} x-4 e^{2 c_1}} \\ y(x)\to \sqrt {-x^2+4 \sqrt {2} e^{c_1} x-4 e^{2 c_1}} \\ y(x)\to -\sqrt {-x^2} \\ y(x)\to \sqrt {-x^2} \\ \end{align*}