63.3.6 problem 4(c)

Internal problem ID [13041]
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)
Date solved : Tuesday, January 28, 2025 at 04:49:59 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.009 (sec). Leaf size: 16

DSolve[Sqrt[t]*D[x[t],t]==Cos[Sqrt[t]],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 2 \sin \left (\sqrt {t}\right )+c_1 \]