75.16.17 problem 490

Internal problem ID [16990]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 490
Date solved : Tuesday, January 28, 2025 at 09:45:18 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)+y(x)=x,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{x} x +c_{1} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 57

DSolve[D[y[x],{x,3}]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]