67.5.3 problem Problem 1(c)
Internal
problem
ID
[14018]
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(c)
Date
solved
:
Monday, March 31, 2025 at 08:22:10 AM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\prime \prime }+3 y^{\prime }+\frac {y}{t}&=t \end{align*}
✓ Maple. Time used: 0.012 (sec). Leaf size: 36
ode:=diff(diff(y(t),t),t)+3*diff(y(t),t)+y(t)/t = t;
dsolve(ode,y(t), singsol=all);
\[
y = \frac {\left (7 \operatorname {KummerU}\left (\frac {2}{3}, 2, 3 t \right ) {\mathrm e}^{-3 t} c_1 +7 \operatorname {KummerM}\left (\frac {2}{3}, 2, 3 t \right ) {\mathrm e}^{-3 t} c_2 +t -\frac {1}{2}\right ) t}{7}
\]
✓ Mathematica. Time used: 21.89 (sec). Leaf size: 253
ode=D[y[t],{t,2}]+3*D[y[t],t]+y[t]/t==t;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\[
y(t)\to G_{1,2}^{2,0}\left (3 t\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right ) \left (\int _1^t-\frac {3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) K[2]^2}{3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right )+3 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {2}{3} \\ 1,1 \\ \end {array} \right .\right )-2 \operatorname {Hypergeometric1F1}\left (\frac {7}{3},3,-3 K[2]\right ) G_{1,2}^{2,0}\left (3 K[2]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}dK[2]+c_2\right )-3 t \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 t\right ) \left (\int _1^t\frac {G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}{-9 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {2}{3} \\ 0,1 \\ \end {array} \right .\right )-9 \operatorname {Hypergeometric1F1}\left (\frac {4}{3},2,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {2}{3} \\ 1,1 \\ \end {array} \right .\right )+6 \operatorname {Hypergeometric1F1}\left (\frac {7}{3},3,-3 K[1]\right ) G_{1,2}^{2,0}\left (3 K[1]\left | \begin {array}{c} \frac {5}{3} \\ 1,2 \\ \end {array} \right .\right )}dK[1]+c_1\right )
\]
✗ Sympy
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq(-t + 3*Derivative(y(t), t) + Derivative(y(t), (t, 2)) + y(t)/t,0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
NotImplementedError : The given ODE Derivative(y(t), t) - (t*(t - Derivative(y(t), (t, 2))) - y(t))/(3*t) cannot be solved by the factorable group method