73.15.54 problem 22.11 (m)

Internal problem ID [15485]
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 (m)
Date solved : Tuesday, January 28, 2025 at 07:59:36 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=3*x^2*exp(5*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{5 x} \left (c_{2} +c_{1} x +\frac {1}{4} x^{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==3*x^2*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{5 x} \left (x^4+4 c_2 x+4 c_1\right ) \]