Internal problem ID [6004]
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]]
\[ \boxed {y^{\prime \prime \prime }=x^{2}+{\mathrm e}^{-x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x$3)=x^2+exp(-x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{5}}{60}+\frac {c_{1} x^{2}}{2}-\frac {\cos \left (x \right ) {\mathrm e}^{-x}}{4}+\frac {\sin \left (x \right ) {\mathrm e}^{-x}}{4}+x c_{2} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 47
DSolve[y'''[x]==x^2+Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^5}{60}+c_3 x^2+\frac {1}{4} e^{-x} \sin (x)-\frac {1}{4} e^{-x} \cos (x)+c_2 x+c_1 \]