78.3.16 problem 5 (d)

Internal problem ID [18119]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 5 (d)
Date solved : Tuesday, January 28, 2025 at 11:28:59 AM
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: 2.305 (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: 60.297 (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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