60.7.93 problem 1684 (book 6.93)

Internal problem ID [11682]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1684 (book 6.93)
Date solved : Tuesday, January 28, 2025 at 06:07:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 2.608 (sec). Leaf size: 25

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

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