56.1.47 problem 47

Internal problem ID [8759]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 47
Date solved : Wednesday, March 05, 2025 at 06:45:59 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t y^{\prime \prime }+4 y^{\prime }&=t^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=t*diff(diff(y(t),t),t)+4*diff(y(t),t) = t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t^{3}}{18}-\frac {c_{1}}{3 t^{3}}+c_{2} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 24

ode=t*D[y[t],{t,2}]+4*D[y[t],t]==t^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^3}{18}-\frac {c_1}{3 t^3}+c_2 \]

✓ Sympy. Time used: 0.208 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 + t*Derivative(y(t), (t, 2)) + 4*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + \frac {C_{2}}{t^{3}} + \frac {t^{3}}{18} \]