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 : Monday, January 27, 2025 at 02:37:09 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)=f(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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