Internal problem ID [2486]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 8.
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 {6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {1}{2}\right ) = 3\right ] \end {align*}
✓ Solution by Maple
Time used: 0.193 (sec). Leaf size: 23
dsolve([(6*x+4*y(x)+1)+(4*x+2*y(x)+2)*diff(y(x),x)=0,y(1/2) = 3],y(x), singsol=all)
\[ y \relax (x ) = -2 x -1+\frac {\sqrt {4 x^{2}+12 x +93}}{2} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 26
DSolve[{(6*x+4*y[x]+1)+(4*x+2*y[x]+2)*y'[x]==0,y[1/2]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-4 x+\sqrt {4 x (x+3)+93}-2\right ) \\ \end{align*}