Internal problem ID [14988]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (y+x \right )^{2} y^{\prime }=a^{2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve((x+y(x))^2*diff(y(x),x)=a^2,y(x), singsol=all)
\[ y \left (x \right ) = a \operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) a -\textit {\_Z} a +c_{1} -x \right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 21
DSolve[(x+y[x])^2*y'[x]==a^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x)-a \arctan \left (\frac {y(x)+x}{a}\right )=c_1,y(x)\right ] \]