Internal problem ID [5251]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-x^{2}-{\mathrm e}^{-x} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 36
dsolve(diff(y(x),x$3)=x^2+exp(-x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{2}}{2}+\frac {x^{5}}{60}-\frac {\cos \relax (x ) {\mathrm e}^{-x}}{4}+\frac {\sin \relax (x ) {\mathrm e}^{-x}}{4}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 41
DSolve[y'''[x]==x^2+Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^5}{60}+c_3 x^2+c_2 x+\frac {1}{4} e^{-x} (\sin (x)-\cos (x))+c_1 \\ \end{align*}