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 : Monday, January 27, 2025 at 03:06:50 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)=3*x+1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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