Internal problem ID [10342]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-t \cos \left (t^{2}\right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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: 0.008 (sec). Leaf size: 15
DSolve[{x'[t]==t*Cos[t^2],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} \left (\sin \left (t^2\right )+2\right ) \\ \end{align*}