73.1.31 problem 2.5 (b i)

Internal problem ID [15009]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.5 (b i)
Date solved : Tuesday, January 28, 2025 at 07:27:29 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

dsolve([diff(y(x),x)=sin(x/2),y(0) = 0],y(x), singsol=all)
 

\[ y = -2 \cos \left (\frac {x}{2}\right )+2 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 19

DSolve[{D[y[x],x]==Sin[x/2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _0^x\sin \left (\frac {K[1]}{2}\right )dK[1] \]