Internal problem ID [5027]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: Example 4.
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 {2 x -4 y+6+\left (x +y-2\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 300
dsolve((2*x-4*y(x)+6)+(x+y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {5}{3}+\frac {\left (12 \sqrt {3}\, \left (3 x -1\right ) \sqrt {\frac {\left (3 x -1\right ) \left (27 \left (3 x -1\right ) c_{1}-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3 x -1\right )^{2} c_{1}^{2}-72 \left (3 x -1\right ) c_{1}+8\right )^{\frac {1}{3}}}{36 c_{1}}-\frac {6 \left (3 x -1\right ) c_{1}-1}{9 c_{1} \left (12 \sqrt {3}\, \left (3 x -1\right ) \sqrt {\frac {\left (3 x -1\right ) \left (27 \left (3 x -1\right ) c_{1}-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3 x -1\right )^{2} c_{1}^{2}-72 \left (3 x -1\right ) c_{1}+8\right )^{\frac {1}{3}}}+\frac {6 \left (3 x -1\right ) c_{1}-1}{9 c_{1}}-\frac {i \sqrt {3}\, \left (\frac {\left (12 \sqrt {3}\, \left (3 x -1\right ) \sqrt {\frac {\left (3 x -1\right ) \left (27 \left (3 x -1\right ) c_{1}-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3 x -1\right )^{2} c_{1}^{2}-72 \left (3 x -1\right ) c_{1}+8\right )^{\frac {1}{3}}}{6 c_{1}}+\frac {4 \left (3 x -1\right ) c_{1}-\frac {2}{3}}{c_{1} \left (12 \sqrt {3}\, \left (3 x -1\right ) \sqrt {\frac {\left (3 x -1\right ) \left (27 \left (3 x -1\right ) c_{1}-4\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3 x -1\right )^{2} c_{1}^{2}-72 \left (3 x -1\right ) c_{1}+8\right )^{\frac {1}{3}}}\right )}{6} \]
✓ Solution by Mathematica
Time used: 60.156 (sec). Leaf size: 2563
DSolve[(2*x-4*y[x]+6)+(x+y[x]-2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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