Internal problem ID [1002]
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: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{2}-3 y x -5 x^{2}}{x^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 23
dsolve([diff(y(x),x)=(y(x)^2-3*x*y(x)-5*x^2)/x^2,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 x^{7}+5 x}{2 x^{6}+1} \]
✓ Solution by Mathematica
Time used: 1.938 (sec). Leaf size: 20
DSolve[{y'[x]==(y[x]^2-3*x*y[x]-5*x^2)/x^2,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\frac {6}{2 x^6+1}-1\right ) \\ \end{align*}