90.20.36 problem 23

Internal problem ID [25331]
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 : 23
Date solved : Friday, October 03, 2025 at 12:00:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {-3+t}\, y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (10\right )&=y_{1} \\ y^{\prime }\left (10\right )&=y_{1} \\ \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+t^(1/2)*diff(y(t),t)-(t-3)^(1/2)*y(t) = 0; 
ic:=[y(10) = y__1, D(y)(10) = y__1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+Sqrt[t]*D[y[t],t]-Sqrt[t-3]*y[t]==0; 
ic={y[10]==y1,Derivative[1][y][10] ==y1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y1 = symbols("y1") 
y = Function("y") 
ode = Eq(sqrt(t)*Derivative(y(t), t) - sqrt(t - 3)*y(t) + Derivative(y(t), (t, 2)),0) 
ics = {y(10): y1, Subs(Derivative(y(t), t), t, 10): y1} 
dsolve(ode,func=y(t),ics=ics)
 

TypeError : Half object cannot be interpreted as an integer