Internal problem ID [999]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y x +y^{2}}{x^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.048 (sec). Leaf size: 21
dsolve([diff(y(x),x)=(x*y(x)+y(x)^2)/x^2,y(-1) = 2],y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 i x}{2 i \ln \relax (x )+i+2 \pi } \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 21
DSolve[{y'[x]==(x*y[x]+y[x]^2)/x^2,y[-1]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x}{2 \log (x)-2 i \pi +1} \\ \end{align*}