75.17.18 problem 568

Internal problem ID [16988]
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, March 13, 2025 at 09:05:43 AM
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: 0.003 (sec). Leaf size: 60

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);
 

\[ y = \frac {\left (\left (-\frac {18 \sin \left (x \right )^{2}}{5}+\frac {9 \cos \left (x \right ) \sin \left (x \right )}{5}+x^{3}+\left (12 c_{2} -\frac {18}{5}\right ) x^{2}+\left (24 c_{3} -\frac {9}{5}\right ) x +24 c_4 \right ) {\mathrm e}^{4 x}+\frac {24 \,{\mathrm e}^{5 x}}{5}-\frac {3 c_{1}}{8}\right ) {\mathrm e}^{-4 x}}{24} \]

✓ Mathematica. Time used: 31.951 (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]
 

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

✓ Sympy. Time used: 0.153 (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)
 

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