81.11.28 problem 15-27

Internal problem ID [21652]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-27
Date solved : Thursday, October 02, 2025 at 07:59:28 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.018 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = 4*exp(-x)+3*exp(2*x); 
ic:=[y(0) = 0, D(y)(0) = -1, (D@@2)(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {9}{2}+\frac {{\mathrm e}^{2 x}}{2}+2 \,{\mathrm e}^{-x} \left (2+x \right ) \]

✗ Mathematica

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

{}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \left (2 x + 4\right ) e^{- x} + \frac {e^{2 x}}{2} - \frac {9}{2} \]