87.12.20 problem 21

Internal problem ID [23468]
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 : 21
Date solved : Thursday, October 02, 2025 at 09:42:06 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 15

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

\[ y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )-\cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to -2 e^x (\cos (x)-\sin (x)) \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (2 \sin {\left (x \right )} - 2 \cos {\left (x \right )}\right ) e^{x} \]