83.27.18 problem 18

Internal problem ID [19293]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 18
Date solved : Monday, March 31, 2025 at 07:05:52 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (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: 0.003 (sec). Leaf size: 43

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

\[ y(x)\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}f(K[1])dK[1]dK[2]dK[3]+x (c_3 x+c_2)+c_1 \]

✓ Sympy. Time used: 0.440 (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)
 

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