Internal problem ID [3357]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 615.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (x -y\right )^{2} y^{\prime }-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve((x-y(x))^2*diff(y(x),x) = a^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (a \ln \left ({\mathrm e}^{\textit {\_Z}}+2 a \right )-a \textit {\_Z} -2 \,{\mathrm e}^{\textit {\_Z}}+2 c_{1}-2 a -2 x \right )}+a +x \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 49
DSolve[(x-y[x])^2 y'[x]==a^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\left (a^2 \left (\frac {\log (a-y(x)+x)}{2 a}-\frac {\log (-a-y(x)+x)}{2 a}\right )\right )-y(x)=c_1,y(x)\right ] \]