Internal problem ID [5780]
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`]]
\[ \boxed {-4 y+\left (x +y-2\right ) y^{\prime }=-2 x -6} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 198
dsolve((2*x-4*y(x)+6)+(x+y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \left (\left (\frac {i \sqrt {3}}{72}-\frac {1}{72}\right ) \left (36 \sqrt {3}\, \left (x -\frac {1}{3}\right ) c_{1}^{2} \sqrt {\frac {243 \left (x -\frac {1}{3}\right )^{2} c_{1} -12 x +4}{c_{1}}}+8+972 \left (x -\frac {1}{3}\right )^{2} c_{1}^{2}+\left (-216 x +72\right ) c_{1} \right )^{\frac {2}{3}}+\left (\frac {1}{18}+\left (-x -\frac {1}{2}\right ) c_{1} \right ) \left (36 \sqrt {3}\, \left (x -\frac {1}{3}\right ) c_{1}^{2} \sqrt {\frac {243 \left (x -\frac {1}{3}\right )^{2} c_{1} -12 x +4}{c_{1}}}+8+972 \left (x -\frac {1}{3}\right )^{2} c_{1}^{2}+\left (-216 x +72\right ) c_{1} \right )^{\frac {1}{3}}+\left (1+i \sqrt {3}\right ) \left (-\frac {1}{18}+\left (x -\frac {1}{3}\right ) c_{1} \right )\right )}{\left (36 \sqrt {3}\, \left (x -\frac {1}{3}\right ) c_{1}^{2} \sqrt {\frac {243 \left (x -\frac {1}{3}\right )^{2} c_{1} -12 x +4}{c_{1}}}+8+972 \left (x -\frac {1}{3}\right )^{2} c_{1}^{2}+\left (-216 x +72\right ) c_{1} \right )^{\frac {1}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.144 (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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