44.1.52 problem 63 (b)

Internal problem ID [6927]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 63 (b)
Date solved : Wednesday, March 05, 2025 at 02:52:47 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \int \left (\int f \left (x \right )d x \right )d x +c_{1} x +c_{2} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 30

ode=D[y[x],{x,2}]==f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.464 (sec). Leaf size: 19

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

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