40.9.5 problem 15

Internal problem ID [6715]
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 : 15
Date solved : Monday, January 27, 2025 at 02:24:41 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 37

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

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