10.2.25 problem 25

Internal problem ID [1153]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 25
Date solved : Monday, January 27, 2025 at 04:36:51 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{3+2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.599 (sec). Leaf size: 18

dsolve([diff(y(x),x) = 2*cos(2*x)/(3+2*y(x)),y(0) = -1],y(x), singsol=all)
 

\[ y = -\frac {3}{2}+\frac {\sqrt {1+4 \sin \left (2 x \right )}}{2} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 23

DSolve[{D[y[x],x] == 2*Cos[2*x]/(3+2*y[x]),y[0]==-1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {4 \sin (2 x)+1}-3\right ) \]