5.4 problem 4

Internal problem ID [12664]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

\[ \boxed {y^{\prime }=x \sin \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 13

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

\[ y(x)\to \sin (x)-x \cos (x) \]