Internal problem ID [1153]
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(e).
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 )+y x +x^{2}-\frac {1}{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 35
dsolve(x^2*(diff(y(x),x)+y(x)^2)+x*y(x)+x^2-1/4=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 i x -1}{2 x}-\frac {{\mathrm e}^{-2 i x}}{c_{1}-\frac {i {\mathrm e}^{-2 i x}}{2}} \]
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 22
DSolve[x^2*(y'[x]+y[x]^2)+x*y[x]+x^2-1/4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2 x}-\tan (x-c_1) \\ \end{align*}