73.15.48 problem 22.11 (g)

Internal problem ID [15479]
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 (g)
Date solved : Tuesday, January 28, 2025 at 07:58:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} {\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 32

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x^2*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{2 x} \left (e^x \left (x^3-3 x^2+6 x-6+3 c_2\right )+3 c_1\right ) \]