81.5.2 problem 2

Internal problem ID [18665]
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 : 2
Date solved : Tuesday, January 28, 2025 at 12:09:01 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)+3*diff(y(x),x)=x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x^{3}}{9}-\frac {4 x^{2}}{9}-\frac {c_{2} {\mathrm e}^{-3 x}}{3}-{\mathrm e}^{-x} c_{1} +\frac {26 x}{27}+c_3 \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 47

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

\[ y(x)\to \frac {x^3}{9}-\frac {4 x^2}{9}+\frac {26 x}{27}-\frac {1}{3} c_1 e^{-3 x}-c_2 e^{-x}+c_3 \]