49.11.8 problem 1(h)

Internal problem ID [7672]
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 : Monday, January 27, 2025 at 03:09:35 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)=x^2+exp(-x)*sin(x),y(x), singsol=all)
 

\[ y = c_3 +\frac {{\mathrm e}^{-x} \left (\sin \left (x \right )-\cos \left (x \right )\right )}{4}+c_{2} x +\frac {c_{1} x^{2}}{2}+\frac {x^{5}}{60} \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 47

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

\[ y(x)\to \frac {x^5}{60}+c_3 x^2+\frac {1}{4} e^{-x} \sin (x)-\frac {1}{4} e^{-x} \cos (x)+c_2 x+c_1 \]