67.5.1 problem Problem 1(a)

Internal problem ID [14016]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 1(a)
Date solved : Monday, March 31, 2025 at 08:22:05 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+y&=t^{7} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=t^2*diff(diff(y(t),t),t)+3*t*diff(y(t),t)+y(t) = t^7; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_2}{t}+\frac {t^{7}}{64}+\frac {c_1 \ln \left (t \right )}{t} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=t^2*D[y[t],{t,2}]+3*t*D[y[t],t]+y[t]==t^7; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^8+64 c_2 \log (t)+64 c_1}{64 t} \]

✓ Sympy. Time used: 0.356 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**7 + t**2*Derivative(y(t), (t, 2)) + 3*t*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1} + C_{2} \log {\left (t \right )} + \frac {t^{8}}{64}}{t} \]