73.15.44 problem 22.11 (c)

Internal problem ID [15475]
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 : 22.11 (c)
Date solved : Tuesday, January 28, 2025 at 07:58:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(-7*x)+2*exp(-7*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-7 x} \left (x^{2}+90 c_{1} {\mathrm e}^{9 x}+90 c_{2} {\mathrm e}^{10 x}+\frac {19 x}{45}+\frac {8371}{4050}\right )}{90} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x^2*Exp[-7*x]+2*Exp[-7*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-7 x} \left (4050 x^2+1710 x+8371\right )}{364500}+c_1 e^{2 x}+c_2 e^{3 x} \]