Internal problem ID [503]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 \cos \left (2 x \right )}{3+2 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.563 (sec). Leaf size: 18
dsolve([diff(y(x),x) = 2*cos(2*x)/(3+2*y(x)),y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {3}{2}+\frac {\sqrt {1+4 \sin \left (2 x \right )}}{2} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 23
DSolve[{y'[x] == 2*Cos[2*x]/(3+2*y[x]),y[0]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\sqrt {4 \sin (2 x)+1}-3\right ) \\ \end{align*}