Internal problem ID [10318]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 61.
Transformation of variables. Page 143
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x^{2} y y^{\prime \prime }+\left (y^{\prime } x -y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(x^2*y(x)*diff(y(x),x$2)+(x*diff(y(x),x)-y(x))^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {-2 x^{2} c_{1}+2 c_{2} x} \\ y \relax (x ) = -\sqrt {-2 x^{2} c_{1}+2 c_{2} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 23
DSolve[x^2*y[x]*y''[x]+(x*y'[x]-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt {x} \sqrt {2 x+c_1} \\ \end{align*}