29.22.9 problem 615

Internal problem ID [5209]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 615
Date solved : Monday, January 27, 2025 at 10:21:03 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 36

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (a \ln \left ({\mathrm e}^{\textit {\_Z}}+2 a \right )-\textit {\_Z} a -2 \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} -2 a -2 x \right )}+a +x \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 49

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

\[ \text {Solve}\left [-\left (a^2 \left (\frac {\log (a-y(x)+x)}{2 a}-\frac {\log (-a-y(x)+x)}{2 a}\right )\right )-y(x)=c_1,y(x)\right ] \]