75.16.40 problem 513

Internal problem ID [17013]
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 : 513
Date solved : Tuesday, January 28, 2025 at 09:45:35 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(y(x),x$3)+diff(y(x),x$2)=1,y(x), singsol=all)
 

\[ y = \frac {x^{2}}{2}+c_{1} {\mathrm e}^{-x}+c_{2} x +c_{3} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{2}+c_3 x+c_1 e^{-x}+c_2 \]