Internal problem ID [1149]
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(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }+y^{2}\right )-x \left (2+x \right ) y+x +2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(x^2*(diff(y(x),x)+y(x)^2)-x*(x+2)*y(x)+x+2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{x}}{-{\mathrm e}^{x}+c_{1}}+\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 49
DSolve[x^2*(y'[x]+y[x])-x*(x+2)+y[x]+x+2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {1}{x}-x} \left (\int _1^x\frac {e^{K[1]-\frac {1}{K[1]}} \left (K[1]^2+K[1]-2\right )}{K[1]^2}dK[1]+c_1\right ) \\ \end{align*}