76.17.22 problem 31

Internal problem ID [17637]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 31
Date solved : Monday, March 31, 2025 at 04:23:19 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y&=t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=t^2*diff(diff(y(t),t),t)+7*t*diff(y(t),t)+5*y(t) = t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {t^{6}+3 c_1 \,t^{4}-4 c_1^{3}+12 c_2}{12 t^{5}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 23

ode=t^2*D[y[t],{t,2}]+7*t*D[y[t],t]+5*y[t]==t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {c_1}{t^5}+\frac {t}{12}+\frac {c_2}{t} \]

✓ Sympy. Time used: 0.232 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) + 7*t*Derivative(y(t), t) - t + 5*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t^{5}} + \frac {C_{2}}{t} + \frac {t}{12} \]