13.2.2 problem 2

Internal problem ID [2300]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:44:57 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 33

dsolve(t^(1/2)*sin(t)*y(t)+diff(y(t),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: 0.054 (sec). Leaf size: 66

DSolve[t^(1/2)*Sin[t]*y[t]+D[y[t],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*}