Internal problem ID [1154]
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(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }+y^{2}\right )-7 y x +7=0} \end {gather*}
✓ Solution by Maple
Time used: 0.193 (sec). Leaf size: 24
dsolve(x^2*(diff(y(x),x)+y(x)^2)-7*x*y(x)+7=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-7 x^{6}+c_{1}}{\left (-x^{6}+c_{1}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 34
DSolve[x^2*(y'[x]+y[x]^2)-7*x*y[x]+7==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {7 x^6-6 c_1}{x^7-6 c_1 x} \\ y(x)\to \frac {1}{x} \\ \end{align*}