Internal problem ID [15260]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 490.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+y=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$3)+y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {x \sqrt {3}}{2}\right )+c_{3} {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {x \sqrt {3}}{2}\right )+{\mathrm e}^{x} x +c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 57
DSolve[y'''[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]