15.11.18 problem 18

Internal problem ID [3128]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 18
Date solved : Monday, January 27, 2025 at 07:22:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 36

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

\[ y = \frac {\left (8 x^{3}-12 x^{2}+9 x -3\right ) {\mathrm e}^{2 x}}{128}+{\mathrm e}^{-2 x} \left (c_{1} x +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 43

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

\[ y(x)\to \frac {1}{128} e^{2 x} \left (8 x^3-12 x^2+9 x-3\right )+e^{-2 x} (c_2 x+c_1) \]