Internal problem ID [3218]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 472.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.312 (sec). Leaf size: 29
dsolve((19+9*x+2*y(x))*diff(y(x),x)+18-2*x-6*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = 4-\frac {-4 \left (3+x \right ) c_{1}+1+\sqrt {-40 \left (3+x \right ) c_{1}+1}}{8 c_{1}} \]
✓ Solution by Mathematica
Time used: 8.446 (sec). Leaf size: 236
DSolve[(19+9 x+2 y[x])y'[x]+18-2 x-6 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} (x+3)-i}}+(1-i)}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} (x+3)-i}}}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} (x+3)+i}}}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {e^{\frac {2 c_1}{9}} (x+3)+i}}+(1-i)}-\frac {19}{2} \\ y(x)\to -2 (x+1) \\ y(x)\to \frac {x+11}{2} \\ \end{align*}