63.3.1 problem 1

Internal problem ID [13036]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page 19
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 04:49:53 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=t \cos \left (t^{2}\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

dsolve([diff(x(t),t)=t*cos(t^2),x(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\sin \left (t^{2}\right )}{2}+1 \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 15

DSolve[{D[x[t],t]==t*Cos[t^2],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} \left (\sin \left (t^2\right )+2\right ) \]