73.15.30 problem 22.10 (c)

Internal problem ID [15461]
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 : 22.10 (c)
Date solved : Tuesday, January 28, 2025 at 07:56:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=6*exp(5*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==6*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

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