40.9.3 problem 13

Internal problem ID [6713]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 13
Date solved : Monday, January 27, 2025 at 02:24:40 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)=5,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 x} c_1}{16}-\frac {5 x^{2}}{8}+c_2 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]==5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {5 x^2}{8}+c_3 x+\frac {1}{16} c_1 e^{4 x}+c_2 \]