Internal problem ID [5790]
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: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {x -2 y+5}{y-2 x -4}=0} \]
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 184
dsolve(diff(y(x),x)=(x-2*y(x)+5)/(y(x)-2*x-4),y(x), singsol=all)
\[ y \left (x \right ) = 2+\frac {\left (x +1\right ) \left (-c_{1}^{2}-c_{1}^{2} \left (-\frac {\left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 \left (x +1\right )^{2} c_{1}^{2}-1}\right )^{\frac {1}{3}}}{6 c_{1} \left (x +1\right )}-\frac {1}{2 c_{1} \left (x +1\right ) \left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 \left (x +1\right )^{2} c_{1}^{2}-1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 \left (x +1\right )^{2} c_{1}^{2}-1}\right )^{\frac {1}{3}}}{3 c_{1} \left (x +1\right )}-\frac {1}{c_{1} \left (x +1\right ) \left (27 c_{1} \left (x +1\right )+3 \sqrt {3}\, \sqrt {27 \left (x +1\right )^{2} c_{1}^{2}-1}\right )^{\frac {1}{3}}}\right )}{2}\right )\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 60.297 (sec). Leaf size: 1601
DSolve[y'[x]==(x-2*y[x]+5)/(y[x]-2*x-4),y[x],x,IncludeSingularSolutions -> True]
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