81.5.13 problem 13

Internal problem ID [18676]
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 : 13
Date solved : Tuesday, January 28, 2025 at 12:09:18 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 22

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{x} \left (\frac {1}{6} x^{3}+c_{1} +c_{2} x +c_3 \,x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 32

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

\[ y(x)\to \frac {1}{6} e^x \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]