Internal problem ID [12321]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {\left (y+2\right ) \left (y-1\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)=sqrt( (y(x)+2)*(y(x)-1)),y(x), singsol=all)
\[ x -\ln \left (y \left (x \right )+\frac {1}{2}+\sqrt {-2+y \left (x \right )^{2}+y \left (x \right )}\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.497 (sec). Leaf size: 41
DSolve[y'[x]==Sqrt[ (y[x]+2)*(y[x]-1)],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-e^{-x-c_1}-9 e^{x+c_1}-2\right ) y(x)\to -2 y(x)\to 1 \end{align*}