15.13.2 problem 2

Internal problem ID [3171]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 22, page 99
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:24:54 AM
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: 0.006 (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)
 

\[ y = {\mathrm e}^{x} \left (\frac {1}{6} x^{3}+c_{1} +c_2 x +c_3 \,x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.009 (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]
 

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