49.1.10 problem 4(a)

Internal problem ID [7589]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 4(a)
Date solved : Sunday, March 30, 2025 at 12:16:16 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=3 x +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x) = 3*x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{2} x^{3}+\frac {1}{2} x^{2}+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} \left (x^3+x^2+2 c_2 x+2 c_1\right ) \]

✓ Sympy. Time used: 0.104 (sec). Leaf size: 17

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

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