Internal problem ID [5028]
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: 31.
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 {y^{\prime }-\frac {2 y-x +5}{2 x -y-4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.385 (sec). Leaf size: 182
dsolve(diff(y(x),x)=(2*y(x)-x+5)/(2*x-y(x)-4),y(x), singsol=all)
\[ y \relax (x ) = -2-\frac {\left (x -1\right ) \left (c_{1}^{2} \left (-\frac {\left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{\frac {1}{3}}}{6 c_{1} \left (x -1\right )}-\frac {1}{2 c_{1} \left (x -1\right ) \left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{\frac {1}{3}}}{3 c_{1} \left (x -1\right )}-\frac {1}{c_{1} \left (x -1\right ) \left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{\frac {1}{3}}}\right )}{2}\right )+c_{1}^{2}\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 1601
DSolve[y'[x]==(2*y[x]-x+5)/(2*x-y[x]-4),y[x],x,IncludeSingularSolutions -> True]
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