73.15.55 problem 22.11 (n)

Internal problem ID [15486]
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 (n)
Date solved : Tuesday, January 28, 2025 at 07:59:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)-10*diff(y(x),x)+25*y(x)=3*x^4,y(x), singsol=all)
 

\[ y = \frac {72}{3125}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{5 x}+\frac {3 x^{4}}{25}+\frac {24 x^{3}}{125}+\frac {108 x^{2}}{625}+\frac {288 x}{3125} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]-10*D[y[x],x]+25*y[x]==3*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 \left (125 x^4+200 x^3+180 x^2+96 x+24\right )}{3125}+c_1 e^{5 x}+c_2 e^{5 x} x \]