77.1.89 problem 116 (page 177)

Internal problem ID [17979]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 116 (page 177)
Date solved : Tuesday, January 28, 2025 at 08:28:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 8.107 (sec). Leaf size: 25

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

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