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 : Saturday, March 29, 2025 at 11:53:52 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

ode:=diff(y(t),t)+1/t^(1/2)*y(t) = exp(1/2*t^(1/2)); 
dsolve(ode,y(t), singsol=all);
 

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

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

ode=D[y[t],t]+1/Sqrt[t]*y[t]==Exp[Sqrt[t]/2]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.200 (sec). Leaf size: 41

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-exp(sqrt(t)/2) + Derivative(y(t), t) + y(t)/sqrt(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 2 \sqrt {t}} + \frac {4 \sqrt {t} e^{\frac {\sqrt {t}}{2}}}{5} - \frac {8 e^{\frac {\sqrt {t}}{2}}}{25} \]