14.1.28 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 : Tuesday, September 30, 2025 at 06:47:48 AM
CAS classification : [[_2nd_order, _quadrature]]

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

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

ode:=diff(diff(y(x),x),x) = x^n; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=D[y[x],{x,2}]==x^n; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.201 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(-x**n + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2} e^{n \log {\left (x \right )}} + \left (C_{1} + C_{2} x\right ) \left (n^{2} + 3 n + 2\right )}{n^{2} + 3 n + 2} \]