68.15.36 problem 36

Internal problem ID [17762]
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 : 36
Date solved : Thursday, October 02, 2025 at 02:27:52 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5 \\ y^{\prime }\left (1\right )&=0 \\ y^{\prime \prime }\left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 20

ode:=x^3*diff(diff(diff(y(x),x),x),x)+15*x^2*diff(diff(y(x),x),x)+54*x*diff(y(x),x)+42*y(x) = 0; 
ic:=[y(1) = 5, D(y)(1) = 0, (D@@2)(y)(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {3}{2 x^{7}}-\frac {35}{2 x^{3}}+\frac {21}{x^{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 24

ode=x^3*D[y[x],{x,3}]+15*x^2*D[y[x],{x,2}]+54*x*D[y[x],x]+42*y[x]==0; 
ic={y[1]==5,Derivative[1][y][1]==0,Derivative[2][y][1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {42 x^5-35 x^4+3}{2 x^7} \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 15*x**2*Derivative(y(x), (x, 2)) + 54*x*Derivative(y(x), x) + 42*y(x),0) 
ics = {y(1): 5, Subs(Derivative(y(x), x), x, 1): 0, Subs(Derivative(y(x), (x, 2)), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {21 - \frac {35}{2 x} + \frac {3}{2 x^{5}}}{x^{2}} \]