47.2.42 problem 40

Internal problem ID [7458]
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
Date solved : Monday, January 27, 2025 at 03:00:51 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.268 (sec). Leaf size: 115

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

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

✓ Solution by Mathematica

Time used: 60.196 (sec). Leaf size: 1601

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

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