Internal problem ID [1051]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (2 x -1\right ) \left (y-1\right )+\left (2+x \right ) \left (x -3\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([((2*x-1)*(y(x)-1))+((x+2)*(x-3))*diff(y(x),x)=0,y(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}-x +6}{\left (2+x \right ) \left (x -3\right )} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 23
DSolve[{((2*x-1)*(y[x]-1))+((x+2)*(x-3))*y'[x]==0,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x-1) x+6}{(x-3) (x+2)} \\ \end{align*}