Internal problem ID [5860]
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]]
\[ \boxed {x^{2} y y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.046 (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 \left (x \right ) = 0 y \left (x \right ) = {\mathrm e}^{-c_{1} x} c_{2} {\mathrm e} x \end{align*}
✓ Solution by Mathematica
Time used: 0.212 (sec). Leaf size: 15
DSolve[x^2*y[x]*y''[x]==x^2*(y'[x])^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x e^{c_1 x} \]