76.1.33 problem 33

Internal problem ID [17332]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 10:01:22 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.378 (sec). Leaf size: 14

dsolve([diff(y(x),x)=2*cos(2*x)/(10+2*y(x)),y(0) = -1],y(x), singsol=all)
 

\[ y = -5+\sqrt {16+\sin \left (2 x \right )} \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 31

DSolve[{D[y[x],x]==2*Cos[2*x]/(10+2*y[x]),{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2} \sqrt {\int _0^x\cos (2 K[1])dK[1]+8}-5 \]