81.5.5 problem 5

Internal problem ID [18668]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 58
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:09:05 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+6*diff(y(x),x)=x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{2}}{12}-\frac {c_{2} {\mathrm e}^{-3 x}}{3}-\frac {{\mathrm e}^{-2 x} c_{1}}{2}-\frac {5 x}{36}+c_3 \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{12}-\frac {5 x}{36}-\frac {1}{3} c_1 e^{-3 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]