6.19.74 problem section 9.3, problem 74

Internal problem ID [2221]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 74
Date solved : Tuesday, September 30, 2025 at 05:25:09 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=0 \\ y^{\prime \prime }\left (0\right )&=-1 \\ y^{\prime \prime \prime }\left (0\right )&=-5 \\ \end{align*}

✓ Maple. Time used: 105.756 (sec). Leaf size: 1461

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)-2*diff(y(x),x) = -2*exp(x)*(cos(x)-sin(x)); 
ic:=[y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = -1, (D@@3)(y)(0) = -5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 3484

ode=1*D[y[x],{x,4}]-3*D[y[x],{x,3}]+5*D[y[x],{x,2}]-2*D[y[x],x]+0*y[x]==-2*Exp[x]*(Cos[x]-Sin[x]); 
ic={y[0]==2,Derivative[1][y][0] ==0,Derivative[2][y][0] ==-1,Derivative[3][y][0]==-5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*sin(x) + 2*cos(x))*exp(x) - 2*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): -1, Subs(Derivative(y(x), (x, 3)), x, 0): -5} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out