Internal problem ID [1003]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-2 x^{2}-y^{2}-4 y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
dsolve([x^2*diff(y(x),x)=2*x^2+y(x)^2+4*x*y(x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-4 x^{2}+3 x}{-3+2 x} \]
✓ Solution by Mathematica
Time used: 0.496 (sec). Leaf size: 19
DSolve[{x^2*y'[x]==2*x^2+y[x]^2+4*x*y[x],y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(3-4 x) x}{2 x-3} \\ \end{align*}