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]
\[ \boxed {\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-y \left (3 x +2\right )=6 x -8} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 31
dsolve((3*x-1)*(diff(y(x),x)+y(x)^2)-(3*x+2)*y(x)-6*x+8=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-c_{1} x +2 \,{\mathrm e}^{3 x -1}+c_{1}}{c_{1} x +{\mathrm e}^{3 x -1}} \]
✓ Solution by Mathematica
Time used: 0.557 (sec). Leaf size: 41
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 \frac {2 \left (-e x+c_1 e^{3 x}+e\right )}{2 e x+c_1 e^{3 x}} y(x)\to 2 \end{align*}