20.12.5 problem Problem 20

Internal problem ID [3799]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 20
Date solved : Monday, January 27, 2025 at 08:02:29 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 49

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+25*diff(y(x),x)=x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (3 c_{1} -4 c_{2} \right ) \cos \left (4 x \right )+4 \left (c_{1} +\frac {3 c_{2}}{4}\right ) \sin \left (4 x \right )\right ) {\mathrm e}^{3 x}}{25}+\frac {x^{3}}{75}+\frac {6 x^{2}}{625}+\frac {22 x}{15625}+c_3 \]

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 71

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+25*D[y[x],x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{75}+\frac {6 x^2}{625}+\frac {22 x}{15625}-\frac {1}{25} (4 c_1-3 c_2) e^{3 x} \cos (4 x)+\frac {1}{25} (3 c_1+4 c_2) e^{3 x} \sin (4 x)+c_3 \]