14.6.1 problem 5 (d)

Internal problem ID [2543]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.1. Algebraic properties of solutions. Excercises page 136
Problem number : 5 (d)
Date solved : Sunday, March 30, 2025 at 12:09:42 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 9

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

\[ y = 2 \sqrt {t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 12

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

\[ y(t)\to 2 \sqrt {t} \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(2*t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) - y(t),0) 
ics = {y(1): 2, Subs(Derivative(y(t), t), t, 1): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 \sqrt {t} \]