90.20.12 problem 14

Internal problem ID [25307]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 5. Second Order Linear Differential Equations. Exercises at page 337
Problem number : 14
Date solved : Thursday, October 02, 2025 at 11:59:49 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

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

\[ y = \frac {3 t^{2} c_2 -4 t^{{3}/{2}}+3 c_1}{3 t} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 25

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

\begin{align*} y(t)&\to -\frac {4 \sqrt {t}}{3}+\frac {c_1}{t}+c_2 t \end{align*}

✓ Sympy. Time used: 0.136 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {C_{1}}{t} + C_{2} t - \frac {4 \sqrt {t}}{3} \]