43.11.8 problem 1(h)

Internal problem ID [8958]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(h)
Date solved : Tuesday, September 30, 2025 at 06:00:32 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=x^{2}+{\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=diff(diff(diff(y(x),x),x),x) = x^2+exp(-x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +\frac {c_1 \,x^{2}}{2}+\frac {x^{5}}{60}+\frac {{\mathrm e}^{-x} \left (-\cos \left (x \right )+\sin \left (x \right )\right )}{4}+c_3 \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 55

ode=D[y[x],{x,3}]==x^2+Exp[-x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}\left (K[1]^2+e^{-K[1]} \sin (K[1])\right )dK[1]dK[2]dK[3]+x (c_3 x+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + Derivative(y(x), (x, 3)) - exp(-x)*sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + \frac {x^{5}}{60} + \frac {e^{- x} \sin {\left (x \right )}}{4} - \frac {e^{- x} \cos {\left (x \right )}}{4} \]