Internal problem ID [10347]
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: 4(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime } \sqrt {t}-\cos \left (\sqrt {t}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(sqrt(t)*diff(x(t),t)=cos(sqrt(t)),x(t), singsol=all)
\[ x \left (t \right ) = 2 \sin \left (\sqrt {t}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 16
DSolve[Sqrt[t]*x'[t]==Cos[Sqrt[t]],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 2 \sin \left (\sqrt {t}\right )+c_1 \\ \end{align*}