69.17.18 problem 568

Internal problem ID [18354]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 568
Date solved : Thursday, October 02, 2025 at 03:10:48 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }&={\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 43

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(diff(y(x),x),x),x) = exp(x)+3*sin(2*x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{24}+\frac {c_2 \,x^{2}}{2}-\frac {{\mathrm e}^{-4 x} c_1}{64}+\frac {3 \sin \left (2 x \right )}{80}+\frac {{\mathrm e}^{x}}{5}+\frac {3 \cos \left (2 x \right )}{40}+c_3 x +c_4 \]

✓ Mathematica. Time used: 20.205 (sec). Leaf size: 78

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

\begin{align*} y(x)&\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{-4 K[2]} \left (c_1+\int _1^{K[2]}e^{4 K[1]} \left (3 \sin (2 K[1])+e^{K[1]}+1\right )dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 46

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{- 4 x} + \frac {x^{3}}{24} + \frac {e^{x}}{5} + \frac {3 \sin {\left (2 x \right )}}{80} + \frac {3 \cos {\left (2 x \right )}}{40} \]