75.16.41 problem 514

Internal problem ID [17014]
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 : 514
Date solved : Tuesday, January 28, 2025 at 09:45:35 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(5*diff(y(x),x$3)-7*diff(y(x),x$2)=3,y(x), singsol=all)
 

\[ y = -\frac {3 x^{2}}{14}+\frac {25 \,{\mathrm e}^{\frac {7 x}{5}} c_{1}}{49}+c_{2} x +c_{3} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-7*D[y[x],{x,2}]==3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3 x^2}{14}+c_3 x+\frac {1}{49} c_1 e^{7 x}+c_2 \]