87.12.17 problem 18

Internal problem ID [23465]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:42:04 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 14

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+4*diff(y(x),x) = 0; 
ic:=[y(0) = 2, D(y)(0) = -1, (D@@2)(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3+\left (x -1\right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 16

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+4*D[y[x],x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} (x-1)+3 \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -1, Subs(Derivative(y(x), (x, 2)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (x - 1\right ) e^{2 x} + 3 \]