Internal problem ID [7809]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 229.
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 {\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3=0} \end {gather*}
✓ Solution by Maple
Time used: 0.985 (sec). Leaf size: 33
dsolve((12*y(x)-5*x-8)*diff(y(x),x)-5*y(x)+2*x+3=0,y(x), singsol=all)
\[ y \relax (x ) = -1-\frac {-\frac {5 \left (4+x \right ) c_{1}}{12}+\frac {\sqrt {\left (4+x \right )^{2} c_{1}^{2}+24}}{12}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 73
DSolve[(12*y[x]-5*x-8)*y'[x]-5*y[x]+2*x+3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \left (5 x-i \sqrt {-x (x+8)-16 (4+9 c_1)}+8\right ) \\ y(x)\to \frac {1}{12} \left (5 x+i \sqrt {-x (x+8)-16 (4+9 c_1)}+8\right ) \\ \end{align*}