47.2.33 problem 31

Internal problem ID [7449]
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
Date solved : Monday, January 27, 2025 at 03:00:14 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 y-x +5}{2 x -y-4} \end{align*}

✓ Solution by Maple

Time used: 0.273 (sec). Leaf size: 115

dsolve(diff(y(x),x)=(2*y(x)-x+5)/(2*x-y(x)-4),y(x), singsol=all)
 

\[ y = -\frac {\left (i \sqrt {3}-1\right ) \left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{{2}/{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}+27 c_{1} x -27 c_{1} \right )^{{1}/{3}} \left (x +1\right ) c_{1}}{6 \left (27 c_{1} \left (x -1\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x -1\right )^{2}-1}\right )^{{1}/{3}} c_{1}} \]

✓ Solution by Mathematica

Time used: 60.183 (sec). Leaf size: 1601

DSolve[D[y[x],x]==(2*y[x]-x+5)/(2*x-y[x]-4),y[x],x,IncludeSingularSolutions -> True]
 

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