75.16.70 problem 543

Internal problem ID [16972]
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. Trial and error method. Exercises page 132
Problem number : 543
Date solved : Monday, March 31, 2025 at 03:36:50 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=x^{2}+x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(y(x),x),x) = x^2+x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{6}-x^{2}+\frac {x^{4}}{12}-\cos \left (x \right ) c_1 -\sin \left (x \right ) c_2 +c_3 x +c_4 \]

✓ Mathematica. Time used: 60.021 (sec). Leaf size: 47

ode=D[y[x],{x,4}]+D[y[x],{x,2}]==x^2+x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.102 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )} + \frac {x^{4}}{12} + \frac {x^{3}}{6} - x^{2} \]