Internal problem ID [3726]
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`]]
\[ \boxed {\left (19+9 x +2 y\right ) y^{\prime }-6 y=-18+2 x} \]
✓ Solution by Maple
Time used: 1.484 (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)
\[ y \left (x \right ) = 4+\frac {4 \left (x +3\right ) c_{1} +\sqrt {-40 \left (x +3\right ) c_{1} +1}-1}{8 c_{1}} \]
✓ Solution by Mathematica
Time used: 16.36 (sec). Leaf size: 276
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 {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-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 {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}}-\frac {19}{2} y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}}-\frac {19}{2} y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-\frac {19}{2} y(x)\to -2 (x+1) y(x)\to \frac {x+11}{2} \end{align*}