20.1.28 problem Problem 36

Internal problem ID [3585]
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
Date solved : Monday, January 27, 2025 at 07:46:38 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

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

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

\[ y \left (x \right ) = \frac {x^{2+n}}{\left (2+n \right ) \left (n +1\right )}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 28

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

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