50.5.14 problem 4(d)

Internal problem ID [7884]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(d)
Date solved : Monday, January 27, 2025 at 03:30:46 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +y-1}{x +4 y+2} \end{align*}

✓ Solution by Maple

Time used: 6.245 (sec). Leaf size: 139

dsolve(diff(y(x),x)=(x+y(x)-1)/(x+4*y(x)+2),y(x), singsol=all)
 

\[ y = \frac {\left (x -4\right ) \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}-16 c_{1} x^{3}+48 c_{1} x^{2}-64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}+8 c_{1} x^{3}-24 c_{1} x^{2}+32 c_{1} x -16 c_{1} \right )^{4}-x +2}{2 \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}-16 c_{1} x^{3}+48 c_{1} x^{2}-64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}+8 c_{1} x^{3}-24 c_{1} x^{2}+32 c_{1} x -16 c_{1} \right )^{4}} \]

✓ Solution by Mathematica

Time used: 60.314 (sec). Leaf size: 8141

DSolve[D[y[x],x]==(x+y[x]-1)/(x+4*y[x]+2),y[x],x,IncludeSingularSolutions -> True]
 

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