Internal problem ID [4379]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {x \left (y y^{\prime \prime }+\left (y^{\prime }\right )^{2}\right )-y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.087 (sec). Leaf size: 35
dsolve(x*(y(x)*diff(y(x),x$2) + diff(y(x),x)^2)= y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {c_{1} x^{2}+2 c_{2}} \\ y \relax (x ) = -\sqrt {c_{1} x^{2}+2 c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 18
DSolve[x*(y[x]*y''[x]+(y'[x])^2)==y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt {x^2+c_1} \\ \end{align*}