78.8.38 problem 38

Internal problem ID [18236]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 11:43:13 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-3 x -2 y-1}{2 x +3 y-1} \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 31

dsolve(diff(y(x),x) = (-3*x-2*y(x)-1)/(2*x+3*y(x)-1),y(x), singsol=all)
 

\[ y = \frac {-2 c_{1} x +c_{1} -\sqrt {-5 \left (x +1\right )^{2} c_{1}^{2}+3}}{3 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 65

DSolve[D[y[x],x] == (-3*x-2*y[x]-1)/(2*x+3*y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-\sqrt {-5 x^2-10 x+1+9 c_1}-2 x+1\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {-5 x^2-10 x+1+9 c_1}-2 x+1\right ) \\ \end{align*}