49.10.4 problem 1(d)

Internal problem ID [7662]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 89
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:09:09 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+6*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=exp(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (\frac {1}{24} x^{4}+c_{1} +c_{2} x +c_3 \,x^{2}+x^{3} c_4 \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 39

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+6*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} e^x \left (x^4+24 c_4 x^3+24 c_3 x^2+24 c_2 x+24 c_1\right ) \]