Internal problem ID [1151]
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(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {\left (1+2 x \right ) \left (y^{\prime }+y^{2}\right )-2 y=2 x +3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve((2*x+1)*(diff(y(x),x)+y(x)^2)-2*y(x)-(2*x+3)=0,y(x), singsol=all)
\[ y \left (x \right ) = -1-\frac {{\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} x}{-\frac {x \left ({\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} x \right )}{1+2 x}-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.403 (sec). Leaf size: 41
DSolve[(2*x+1)*(y'[x]+y[x]^2)-2*y[x]-(2*x+3)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{2 x+1} (x+1)-c_1}{e^{2 x+1} x+c_1} y(x)\to -1 \end{align*}