71.5.4 problem 4

Internal problem ID [14400]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 06:29:46 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 12

dsolve([diff(y(x),x)=x*sin(x),y(1/2*Pi) = 1],y(x), singsol=all)
 

\[ y = \sin \left (x \right )-\cos \left (x \right ) x \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 24

DSolve[{D[y[x],x]==x*Sin[x],{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _{\frac {\pi }{2}}^xK[1] \sin (K[1])dK[1]+1 \]