Internal problem ID [2105]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x^{n}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)=x^n,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2+n}}{\left (2+n \right ) \left (n +1\right )}+x c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 28
DSolve[y''[x]==x^n,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{n+2}}{n^2+3 n+2}+c_2 x+c_1 \\ \end{align*}