Internal problem ID [3356]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 614.
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: 24
dsolve((x+y(x))^2*diff(y(x),x) = a^2,y(x), singsol=all)
\[ y \relax (x ) = a \RootOf \left (\tan \left (\textit {\_Z} \right ) a -a \textit {\_Z} +c_{1}-x \right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 21
DSolve[(x+y[x])^2 y'[x]==a^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-a \text {ArcTan}\left (\frac {y(x)+x}{a}\right )=c_1,y(x)\right ] \]