75.16.19 problem 492

Internal problem ID [16992]
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 : 492
Date solved : Tuesday, January 28, 2025 at 09:45:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)+diff(y(x),x)=2,y(x), singsol=all)
 

\[ y = -\cos \left (x \right ) c_{2} +\sin \left (x \right ) c_{1} +2 x +c_{3} \]

✓ Solution by Mathematica

Time used: 60.008 (sec). Leaf size: 29

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

\[ y(x)\to \int _1^x(c_1 \cos (K[1])+c_2 \sin (K[1])+2)dK[1]+c_3 \]