68.15.66 problem 65

Internal problem ID [17792]
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 : 65
Date solved : Thursday, October 02, 2025 at 02:28:17 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ y^{\prime }\left (1\right )&=10 \\ y^{\prime \prime }\left (1\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.084 (sec). Leaf size: 25

ode:=x^3*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)+44*x*diff(y(x),x)+58*y(x) = 0; 
ic:=[y(1) = 2, D(y)(1) = 10, (D@@2)(y)(1) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\frac {106}{25}+\frac {14 \sin \left (5 \ln \left (x \right )\right )}{5}-\frac {56 \cos \left (5 \ln \left (x \right )\right )}{25}}{x^{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=x^3*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]+44*x*D[y[x],x]+58*y[x]==0; 
ic={y[1]==2,Derivative[1][y][1]==10,Derivative[2][y][1]==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {70 \sin (5 \log (x))-56 \cos (5 \log (x))+106}{25 x^2} \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 9*x**2*Derivative(y(x), (x, 2)) + 44*x*Derivative(y(x), x) + 58*y(x),0) 
ics = {y(1): 2, Subs(Derivative(y(x), x), x, 1): 10, Subs(Derivative(y(x), (x, 2)), x, 1): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\frac {14 \sin {\left (5 \log {\left (x \right )} \right )}}{5} - \frac {56 \cos {\left (5 \log {\left (x \right )} \right )}}{25} + \frac {106}{25}}{x^{2}} \]