12.9.41 problem 38 part (f)

Internal problem ID [1797]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 38 part (f)
Date solved : Monday, January 27, 2025 at 05:35:04 AM
CAS classification : [_quadrature]

\begin{align*} 6 y^{\prime }+6 y^{2}-y-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 24

dsolve(6*diff(y(x),x)+6*y(x)^2-y(x)-1=0,y(x), singsol=all)
 

\[ y = \frac {1+{\mathrm e}^{\frac {5 x}{6}} c_1}{2 \,{\mathrm e}^{\frac {5 x}{6}} c_1 -3} \]

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 56

DSolve[6*D[y[x],x]+6*y[x]^2-y[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{5 x/6}-e^{5 c_1}}{2 e^{5 x/6}+3 e^{5 c_1}} \\ y(x)\to -\frac {1}{3} \\ y(x)\to \frac {1}{2} \\ \end{align*}