Internal problem ID [1650]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(t^(1/2)*sin(t)*y(t)+diff(y(t),t) = 0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{\sqrt {t}\, \cos \left (t \right )-\frac {\operatorname {FresnelC}\left (\sqrt {2}\, \sqrt {\frac {t}{\pi }}\right ) \sqrt {\pi }\, \sqrt {2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 47
DSolve[t^(1/2)*Sin[t]*y[t]+y'[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \exp \left (-\frac {1}{2} i t^{3/2} \left (\operatorname {ExpIntegralE}\left (-\frac {1}{2},-i t\right )-\operatorname {ExpIntegralE}\left (-\frac {1}{2},i t\right )\right )\right ) \\ y(t)\to 0 \\ \end{align*}