Internal problem ID [5107]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.33.
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 }-x^{2} \left (y^{\prime }\right )^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.08 (sec). Leaf size: 19
dsolve(x^2*y(x)*diff(y(x),x$2)=x^2*(diff(y(x),x))^2-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = {\mathrm e}^{-c_{1} x} c_{2} {\mathrm e} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 15
DSolve[x^2*y[x]*y''[x]==x^2*(y'[x])^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x e^{c_1 x} \\ \end{align*}