1.2 problem 1 (b)

Internal problem ID [5160]

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 (b).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _quadrature]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2-x=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

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

\[ y \relax (x ) = \frac {1}{6} x^{3}+x^{2}+c_{1} x +c_{2} \]

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

DSolve[y''[x]==2+x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^3}{6}+x^2+c_2 x+c_1 \\ \end{align*}