Internal problem ID [3708]
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`]]
\[ \boxed {\left (6-4 x -y\right ) y^{\prime }+y=2 x} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 198
dsolve((6-4*x-y(x))*diff(y(x),x) = 2*x-y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {2}{3}}}{12}-\left (\frac {1}{3}+\left (x -3\right ) c_{1} \right ) \left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {1}{3}}+2 \left (-1-i \sqrt {3}\right ) \left (-\frac {1}{6}+c_{1} \left (x -1\right )\right )}{\left (12 \sqrt {3}\, c_{1}^{2} \left (x -1\right ) \sqrt {\frac {27 \left (x -1\right )^{2} c_{1} -4 x +4}{c_{1}}}+8+108 \left (x -1\right )^{2} c_{1}^{2}+\left (-72 x +72\right ) c_{1} \right )^{\frac {1}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.097 (sec). Leaf size: 2581
DSolve[(6-4 x-y[x])y'[x]==2 x -y[x],y[x],x,IncludeSingularSolutions -> True]
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