Internal problem ID [3238]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 492.
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 (5-x +6 y\right ) y^{\prime }-3+x -4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.985 (sec). Leaf size: 29
dsolve((5-x+6*y(x))*diff(y(x),x) = 3-x+4*y(x),y(x), singsol=all)
\[ y \relax (x ) = -1-\frac {-4 \left (x +1\right ) c_{1}+3+\sqrt {-8 \left (x +1\right ) c_{1}+9}}{8 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.088 (sec). Leaf size: 377
DSolve[(5-x+6 y[x])y'[x]==3-x+4 y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (x+\frac {2}{\frac {1}{x+1}+\sqrt {\frac {1}{(x+1)^2+e^{\frac {4 c_1}{9}} (x+1)^4}-\sqrt {-\frac {1}{2 (x+1)^4+e^{\frac {4 c_1}{9}} (x+1)^6+e^{-\frac {4 c_1}{9}} (x+1)^2}}}}-5\right ) \\ y(x)\to \frac {1}{6} \left (x+\frac {2}{\frac {1}{x+1}-\sqrt {\frac {1}{(x+1)^2+e^{\frac {4 c_1}{9}} (x+1)^4}-\sqrt {-\frac {1}{2 (x+1)^4+e^{\frac {4 c_1}{9}} (x+1)^6+e^{-\frac {4 c_1}{9}} (x+1)^2}}}}-5\right ) \\ y(x)\to \frac {1}{6} \left (x+\frac {2}{\frac {1}{x+1}+\sqrt {\sqrt {-\frac {1}{2 (x+1)^4+e^{\frac {4 c_1}{9}} (x+1)^6+e^{-\frac {4 c_1}{9}} (x+1)^2}}+\frac {1}{(x+1)^2+e^{\frac {4 c_1}{9}} (x+1)^4}}}-5\right ) \\ y(x)\to \frac {1}{6} \left (x+\frac {2}{\frac {1}{x+1}-\sqrt {\sqrt {-\frac {1}{2 (x+1)^4+e^{\frac {4 c_1}{9}} (x+1)^6+e^{-\frac {4 c_1}{9}} (x+1)^2}}+\frac {1}{(x+1)^2+e^{\frac {4 c_1}{9}} (x+1)^4}}}-5\right ) \\ \end{align*}