Internal problem ID [12405]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number: 10 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {\left (y+2\right ) \left (y-1\right )}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 34
dsolve([diff(y(x),x)=sqrt( (y(x)+2)*( y(x)-1)),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {i {\mathrm e}^{x} \sqrt {2}}{2}+\frac {{\mathrm e}^{x}}{4}-\frac {i \sqrt {2}\, {\mathrm e}^{-x}}{2}-\frac {1}{2}+\frac {{\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 45
DSolve[{y'[x]==Sqrt[ (y[x]+2)*( y[x]-1)],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-x} \left (e^x-1\right ) \left (\left (1+2 i \sqrt {2}\right ) e^x-1+2 i \sqrt {2}\right ) \]