20.1.31 problem Problem 39

Internal problem ID [3588]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 39
Date solved : Sunday, March 30, 2025 at 01:53:33 AM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=6 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=-4 \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 19

ode:=diff(diff(diff(y(x),x),x),x) = 6*x; 
ic:=y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {1}{4} x^{4}-2 x^{2}+1-x \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

ode=D[y[x],{x,3}]==6*x; 
ic={y[0]==2,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==-4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (x^4-8 x^2-4 x+8\right ) \]

✓ Sympy. Time used: 0.090 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): -1, Subs(Derivative(y(x), (x, 2)), x, 0): -4} 
dsolve(ode,func=y(x),ics=ics)
 

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