29.30.34 problem 894

Internal problem ID [5474]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 894
Date solved : Monday, January 27, 2025 at 11:25:23 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

\begin{align*} y \left (x \right ) &= x \left (c_{1} -\ln \left (x \right )\right ) \\ y \left (x \right ) &= \frac {x}{2}+\frac {c_{1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \frac {x}{2}+\frac {c_1}{x} \\ y(x)\to x (-\log (x)+c_1) \\ \end{align*}