Internal problem ID [5463]
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]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +y-1}{x +4 y+2}=0} \end {gather*}
✓ Solution by Maple
Time used: 2.171 (sec). Leaf size: 65
dsolve(diff(y(x),x)=(x+y(x)-1)/(x+4*y(x)+2),y(x), singsol=all)
\[ y \relax (x ) = -1+\frac {\left (x -2\right ) \left (\RootOf \left (\textit {\_Z}^{16}+2 \left (x -2\right )^{4} c_{1} \textit {\_Z}^{4}-\left (x -2\right )^{4} c_{1}\right )^{4}-1\right )}{2 \RootOf \left (\textit {\_Z}^{16}+2 \left (x -2\right )^{4} c_{1} \textit {\_Z}^{4}-\left (x -2\right )^{4} c_{1}\right )^{4}} \]
✓ Solution by Mathematica
Time used: 60.503 (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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