76.48.20 problem Ex. 20

Internal problem ID [20286]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 20
Date solved : Thursday, October 02, 2025 at 05:41:02 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\[ y = \int \left (\int \int f \left (x \right )d x d x +c_1 x \right )d x +c_2 x +c_3 \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 43

ode=D[y[x],{x,3}]==f[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]}f(K[1])dK[1]dK[2]dK[3]+x (c_3 x+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.281 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} + x^{2} \left (C_{3} + \frac {\int f{\left (x \right )}\, dx}{2}\right ) + x \left (C_{2} - \int x f{\left (x \right )}\, dx\right ) + \frac {\int x^{2} f{\left (x \right )}\, dx}{2} \]