Internal problem ID [7859]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 280.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (x +y\right )^{2} y^{\prime }-a^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve((y(x)+x)^2*diff(y(x),x)-a^2=0,y(x), singsol=all)
\[ y \left (x \right ) = a \operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) a -a \textit {\_Z} +c_{1} -x \right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 21
DSolve[(y[x]+x)^2*y'[x]-a^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-a \arctan \left (\frac {y(x)+x}{a}\right )=c_1,y(x)\right ] \]