Internal problem ID [15020]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 113.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {4 y+\left (4 x +2 y+1\right ) y^{\prime }=-8 x -1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve((8*x+4*y(x)+1)+(4*x+2*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y &= -2 x -\frac {1}{2}-\frac {\sqrt {-4 c_{1} +4 x +1}}{2} \\ y &= -2 x -\frac {1}{2}+\frac {\sqrt {-4 c_{1} +4 x +1}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 55
DSolve[(8*x+4*y[x]+1)+(4*x+2*y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-4 x-\sqrt {4 x+1+4 c_1}-1\right ) \\ y(x)\to \frac {1}{2} \left (-4 x+\sqrt {4 x+1+4 c_1}-1\right ) \\ \end{align*}