13.2.17 problem 21

Internal problem ID [2315]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 21
Date solved : Monday, January 27, 2025 at 05:45:27 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{\sqrt {t}}&={\mathrm e}^{\frac {\sqrt {t}}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(t),t)+1/sqrt(t)*y(t)=exp(sqrt(t)/2),y(t), singsol=all)
 

\[ y = \frac {\left (20 \,{\mathrm e}^{\frac {5 \sqrt {t}}{2}} \sqrt {t}-8 \,{\mathrm e}^{\frac {5 \sqrt {t}}{2}}+25 c_1 \right ) {\mathrm e}^{-2 \sqrt {t}}}{25} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 42

DSolve[D[y[t],t]+1/Sqrt[t]*y[t]==Exp[Sqrt[t]/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {4}{25} e^{\frac {\sqrt {t}}{2}} \left (5 \sqrt {t}-2\right )+c_1 e^{-2 \sqrt {t}} \]