Internal problem ID [949]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right ) \left (-2+x \right ) y^{\prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -3] \end {align*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 22
dsolve([(x+1)*(x-2)*diff(y(x),x)+y(x)=0,y(1) = -3],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3 \,2^{\frac {2}{3}} \left (1+i \sqrt {3}\right ) \left (x +1\right )^{\frac {1}{3}}}{4 \left (-2+x \right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 23
DSolve[{(x+1)*(x-2)*y'[x]+y[x]==0,y[1]==-3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3 \sqrt [3]{x+1}}{\sqrt [3]{4-2 x}} \\ \end{align*}