74.15.38 problem 38

Internal problem ID [16398]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 38
Date solved : Thursday, March 13, 2025 at 08:12:29 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2\\ y^{\prime }\left (1\right )&=0\\ y^{\prime \prime }\left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 24

ode:=x^3*diff(diff(diff(y(x),x),x),x)-6*x^2*diff(diff(y(x),x),x)+17*x*diff(y(x),x)-17*y(x) = 0; 
ic:=y(1) = -2, D(y)(1) = 0, (D@@2)(y)(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {17 x}{5}+\frac {\left (-11 \sin \left (\ln \left (x \right )\right )+7 \cos \left (\ln \left (x \right )\right )\right ) x^{4}}{5} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 28

ode=x^3*D[y[x],{x,3}]-6*x^2*D[y[x],{x,2}]+17*x*D[y[x],x]-17*y[x]==0; 
ic={y[1]==-2,Derivative[1][y][1]==0,Derivative[2][y][1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} x \left (-11 x^3 \sin (\log (x))+7 x^3 \cos (\log (x))-17\right ) \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 6*x**2*Derivative(y(x), (x, 2)) + 17*x*Derivative(y(x), x) - 17*y(x),0) 
ics = {y(1): -2, Subs(Derivative(y(x), x), x, 1): 0, Subs(Derivative(y(x), (x, 2)), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (x^{3} \left (- \frac {11 \sin {\left (\log {\left (x \right )} \right )}}{5} + \frac {7 \cos {\left (\log {\left (x \right )} \right )}}{5}\right ) - \frac {17}{5}\right ) \]