73.1.32 problem 2.5 (b ii)

Internal problem ID [15010]
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 ii)
Date solved : Tuesday, January 28, 2025 at 07:27:30 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 )&=3 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(x),x)=sin(x/2),y(0) = 3],y(x), singsol=all)
 

\[ y = -2 \cos \left (\frac {x}{2}\right )+5 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 21

DSolve[{D[y[x],x]==Sin[x/2],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _0^x\sin \left (\frac {K[1]}{2}\right )dK[1]+3 \]