90.20.7 problem 7

Internal problem ID [25302]
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 : 7
Date solved : Thursday, October 02, 2025 at 11:59:46 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(t), t) - (sqrt(t) - y(t) - Derivative(y(t), (t, 2))