12.9.43 problem 39 part(a)

Internal problem ID [1799]
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)
Date solved : Monday, January 27, 2025 at 05:35:07 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )-x \left (x +2\right ) y+x +2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 26

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

\[ y = \frac {x \,{\mathrm e}^{x}+{\mathrm e}^{x}-c_1}{\left (-c_1 +{\mathrm e}^{x}\right ) x} \]

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 49

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

\[ y(x)\to e^{\frac {1}{x}-x} \left (\int _1^x\frac {e^{K[1]-\frac {1}{K[1]}} \left (K[1]^2+K[1]-2\right )}{K[1]^2}dK[1]+c_1\right ) \]