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]
\[ \boxed {x^{2} \left (y^{\prime }+y^{2}\right )+y x=-x^{2}+\frac {1}{4}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 46
dsolve(x^2*(diff(y(x),x)+y(x)^2)+x*y(x)+x^2-1/4=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-4 c_{1} x -{\mathrm e}^{-2 i x}-2 i {\mathrm e}^{-2 i x} x -2 i c_{1}}{2 x \left ({\mathrm e}^{-2 i x}+2 i c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.377 (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]
\[ y(x)\to -\frac {1}{2 x}-\tan (x-c_1) \]