69.14.2 problem 328

Internal problem ID [18203]
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 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 328
Date solved : Thursday, October 02, 2025 at 03:09:01 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=x +\cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {x^{4}}{24}+\frac {c_1 \,x^{2}}{2}-\sin \left (x \right )+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 46

ode=D[y[x],{x,3}]==x+Cos[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}(\cos (K[1])+K[1])dK[1]dK[2]dK[3]+x (c_3 x+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 20

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

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