49.1.3 problem 1 (d)

Internal problem ID [7582]
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 : 1 (d)
Date solved : Monday, January 27, 2025 at 03:06:36 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$3)=x^2,y(x), singsol=all)
 

\[ y = \frac {1}{60} x^{5}+\frac {1}{2} c_{1} x^{2}+c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 25

DSolve[D[y[x],{x,3}]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^5}{60}+c_3 x^2+c_2 x+c_1 \]