23.3.15 problem 8(e)

Internal problem ID [4156]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 8(e)
Date solved : Monday, January 27, 2025 at 08:40:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

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

\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (c_{2} +c_{1} x +\frac {1}{20} x^{5}+\frac {1}{6} x^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{60} e^{2 x} \left (3 x^5+10 x^3+60 c_2 x+60 c_1\right ) \]