14.1.2 problem 2

Internal problem ID [2473]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:53:36 AM
CAS classification : [_separable]

\begin{align*} \sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(t),t)+y(t)*sqrt(t)*sin(t)=0,y(t), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{\sqrt {t}\, \cos \left (t \right )-\frac {\sqrt {2}\, \sqrt {\pi }\, \operatorname {FresnelC}\left (\frac {\sqrt {2}\, \sqrt {t}}{\sqrt {\pi }}\right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 66

DSolve[D[y[t],t]+y[t]*Sqrt[t]*Sin[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to c_1 \exp \left (\frac {i \left (\sqrt {-i t} \Gamma \left (\frac {3}{2},-i t\right )-\sqrt {i t} \Gamma \left (\frac {3}{2},i t\right )\right )}{2 \sqrt {t}}\right ) \\ y(t)\to 0 \\ \end{align*}