48.3.4 problem Example 3.33

Internal problem ID [7528]
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
Date solved : Tuesday, January 28, 2025 at 03:16:30 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x^{2} y y^{\prime \prime }&=x^{2} {y^{\prime }}^{2}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.016 (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 &= 0 \\ y &= c_{2} x \,{\mathrm e}^{-c_{1} x +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 15

DSolve[x^2*y[x]*D[y[x],{x,2}]==x^2*(D[y[x],x])^2-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x e^{c_1 x} \]