Internal problem ID [1012]
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: 35(a).
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}-y^{2}-y x +4 x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.261 (sec). Leaf size: 19
dsolve([x^2*diff(y(x),x)=y(x)^2+x*y(x)-4*x^2,y(-1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 x^{5}+2 x}{x^{4}+1} \]
✓ Solution by Mathematica
Time used: 0.583 (sec). Leaf size: 18
DSolve[{x^2*y'[x]==y[x]^2+x*y[x]-4*x^2,y[-1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\frac {4}{x^4+1}-2\right ) \\ \end{align*}