Internal problem ID [13274]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\sin \left (\frac {x}{2}\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([diff(y(x),x)=sin(x/2),y(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = -2 \cos \left (\frac {x}{2}\right )+5 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 15
DSolve[{y'[x]==Sin[x/2],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 5-2 \cos \left (\frac {x}{2}\right ) \]