87.12.16 problem 17

Internal problem ID [23464]
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 : 17
Date solved : Thursday, October 02, 2025 at 09:42:04 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=3 \\ y^{\prime \prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 11

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

\[ y = -1+x +2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 13

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

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

✓ Sympy. Time used: 0.046 (sec). Leaf size: 10

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

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