62.37.2 problem Ex 2

Internal problem ID [13009]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 61. Transformation of variables. Page 143
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 08:24:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x^{3} y^{\prime \prime }-\left (-y+x y^{\prime }\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$2)-(x*diff(y(x),x)-y(x))^2=0,y(x), singsol=all)
 

\[ y = -x \ln \left (\frac {c_{1} x -c_{2}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.774 (sec). Leaf size: 21

DSolve[x^3*D[y[x],{x,2}]-(x*D[y[x],x]-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \log \left (-\frac {c_2 x+c_1}{x}\right ) \]