Internal problem ID [5860]
Internal file name [OUTPUT/5108_Sunday_June_05_2022_03_24_53_PM_20418152/index.tex]
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.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
Unable to solve or complete the solution.
\[ \boxed {x^{2} y y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+y^{2}=0} \]
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying a quadrature <- quadrature successful <- 2nd order, 2 integrating factors of the form mu(x,y) successful`
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
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 ) &= c_{2} x \,{\mathrm e}^{-c_{1} x +1} \\ \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]
\[ y(x)\to c_2 x e^{c_1 x} \]