Internal problem ID [2483]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 32
dsolve((5*x+2*y(x)+1)+(2*x+y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -3-\frac {2 c_{1} \left (x -1\right )+\sqrt {-\left (x -1\right )^{2} c_{1}^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 49
DSolve[(5*x+2*y[x]+1)+(2*x+y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x-\sqrt {-((x-2) x)+1+c_1}-1 \\ y(x)\to -2 x+\sqrt {-((x-2) x)+1+c_1}-1 \\ \end{align*}