Internal problem ID [6216]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-1+y+x}{x +4 y+2}=0} \]
✓ Solution by Maple
Time used: 4.563 (sec). Leaf size: 139
dsolve(diff(y(x),x)=(x+y(x)-1)/(x+4*y(x)+2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x -4\right ) \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}-16 c_{1} x^{3}+48 c_{1} x^{2}-64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}+8 c_{1} x^{3}-24 c_{1} x^{2}+32 c_{1} x -16 c_{1} \right )^{4}-x +2}{2 \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}-16 c_{1} x^{3}+48 c_{1} x^{2}-64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}+8 c_{1} x^{3}-24 c_{1} x^{2}+32 c_{1} x -16 c_{1} \right )^{4}} \]
✓ Solution by Mathematica
Time used: 60.343 (sec). Leaf size: 8141
DSolve[y'[x]==(x+y[x]-1)/(x+4*y[x]+2),y[x],x,IncludeSingularSolutions -> True]
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