68.15.35 problem 35

Internal problem ID [17761]
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 : 35
Date solved : Thursday, October 02, 2025 at 02:27:51 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 18

ode:=x^3*diff(diff(diff(y(x),x),x),x)+10*x^2*diff(diff(y(x),x),x)-20*x*diff(y(x),x)+20*y(x) = 0; 
ic:=[y(1) = 0, D(y)(1) = -1, (D@@2)(y)(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3 x^{2}}{4}+\frac {1}{44 x^{10}}+\frac {8 x}{11} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=x^3*D[y[x],{x,3}]+10*x^2*D[y[x],{x,2}]-20*x*D[y[x],x]+20*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1]==-1,Derivative[2][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{44 x^{10}}-\frac {3 x^2}{4}+\frac {8 x}{11} \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 10*x**2*Derivative(y(x), (x, 2)) - 20*x*Derivative(y(x), x) + 20*y(x),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): -1, Subs(Derivative(y(x), (x, 2)), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {3 x^{2}}{4} + \frac {8 x}{11} + \frac {1}{44 x^{10}} \]