Internal problem ID [2828]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (\left (3 c_{1} -4 c_{2} \right ) \cos \left (4 x \right )+4 \sin \left (4 x \right ) \left (c_{1} +\frac {3 c_{2}}{4}\right )\right ) {\mathrm e}^{3 x}}{25}+\frac {x^{3}}{75}+\frac {6 x^{2}}{625}+\frac {22 x}{15625}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.272 (sec). Leaf size: 71
DSolve[y'''[x]-6*y''[x]+25*y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{75}+\frac {6 x^2}{625}+\frac {22 x}{15625}-\frac {1}{25} (4 c_1-3 c_2) e^{3 x} \cos (4 x)+\frac {1}{25} (3 c_1+4 c_2) e^{3 x} \sin (4 x)+c_3 \]