73.15.12 problem 22.5 (b)

Internal problem ID [15443]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.5 (b)
Date solved : Tuesday, January 28, 2025 at 07:55:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=x^3,y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-5 x} \left (\left (x^{3}+\frac {12}{5} x^{2}+\frac {126}{25} x +\frac {624}{125}\right ) {\mathrm e}^{5 x}-5 \,{\mathrm e}^{6 x} c_{2} -5 c_{1} \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]+4*D[y[x],x]-5*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{625} \left (-125 x^3-300 x^2-630 x-624\right )+c_1 e^{-5 x}+c_2 e^x \]