Internal problem ID [978]
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: Example 3(b).
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 +x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.057 (sec). Leaf size: 19
dsolve([x^2*diff(y(x),x)=y(x)^2+x*y(x)-x^2,y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (x^{2}+3\right )}{x^{2}-3} \]
✓ Solution by Mathematica
Time used: 0.517 (sec). Leaf size: 20
DSolve[{x^2*y'[x]==y[x]^2+x*y[x]-x^2,y[1]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x \left (x^2+3\right )}{x^2-3} \\ \end{align*}