9.46 problem 39 part(d)

Internal problem ID [1152]

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: 39 part(d).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_rational, _Riccati]

Solve \begin {gather*} \boxed {\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (3 x +2\right ) y-6 x +8=0} \end {gather*}

Solution by Maple

Time used: 0.062 (sec). Leaf size: 33

dsolve((3*x-1)*(diff(y(x),x)+y(x)^2)-(3*x+2)*y(x)-6*x+8=0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {2 \,{\mathrm e}^{3 x -1}+\left (1-x \right ) c_{1}}{x c_{1}+{\mathrm e}^{3 x -1}} \]

Solution by Mathematica

Time used: 0.505 (sec). Leaf size: 34

DSolve[(3*x-1)*(y'[x]+y[x]^2)-(3*x+2)*y[x]-6*x+8==0,y[x],x,IncludeSingularSolutions -> True]
 

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