Internal problem ID [3200]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 454.
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 (6-4 x -y\right ) y^{\prime }-2 x +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 254
dsolve((6-4*x-y(x))*diff(y(x),x) = 2*x-y(x),y(x), singsol=all)
\[ y \relax (x ) = 2+\frac {\left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 c_{1} \left (x -1\right )-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (x -1\right )^{2} c_{1}^{2}-72 c_{1} \left (x -1\right )+8\right )^{\frac {1}{3}}}{12 c_{1}}-\frac {6 c_{1} \left (x -1\right )-1}{3 c_{1} \left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 c_{1} \left (x -1\right )-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (x -1\right )^{2} c_{1}^{2}-72 c_{1} \left (x -1\right )+8\right )^{\frac {1}{3}}}-\frac {3 c_{1} \left (x -1\right )+1}{3 c_{1}}-\frac {i \sqrt {3}\, \left (\frac {\left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 c_{1} \left (x -1\right )-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (x -1\right )^{2} c_{1}^{2}-72 c_{1} \left (x -1\right )+8\right )^{\frac {1}{3}}}{6 c_{1}}+\frac {4 c_{1} \left (x -1\right )-\frac {2}{3}}{c_{1} \left (12 \sqrt {3}\, \left (x -1\right ) \sqrt {\frac {\left (x -1\right ) \left (27 c_{1} \left (x -1\right )-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (x -1\right )^{2} c_{1}^{2}-72 c_{1} \left (x -1\right )+8\right )^{\frac {1}{3}}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 79.002 (sec). Leaf size: 2563
DSolve[(6-4 x-y[x])y'[x]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
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