Internal problem ID [12131]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 y-x -4}{2 x -y+5}=0} \]
✓ Solution by Maple
Time used: 0.891 (sec). Leaf size: 117
dsolve(diff(y(x),x)=(2*y(x)-x-4)/(2*x-y(x)+5),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (i \sqrt {3}-1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}+27 c_{1} \left (x +2\right )\right )^{\frac {2}{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}+27 c_{1} x +54 c_{1} \right )^{\frac {1}{3}} \left (1+x \right ) c_{1}}{6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}+27 c_{1} \left (x +2\right )\right )^{\frac {1}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.277 (sec). Leaf size: 1624
DSolve[y'[x]==(2*y[x]-x-4)/(2*x-y[x]+5),y[x],x,IncludeSingularSolutions -> True]
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