Internal problem ID [2319]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 63
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+25*diff(y(x),x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \,{\mathrm e}^{3 x} \cos \left (4 x \right ) c_{1}}{25}+\frac {4 c_{1} {\mathrm e}^{3 x} \sin \left (4 x \right )}{25}-\frac {4 c_{2} {\mathrm e}^{3 x} \cos \left (4 x \right )}{25}+\frac {3 \,{\mathrm e}^{3 x} \sin \left (4 x \right ) c_{2}}{25}+\frac {6 x^{2}}{625}+\frac {x^{3}}{75}+\frac {22 x}{15625}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 61
DSolve[y'''[x]-6*y''[x]+25*y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (25 x (25 x+18)+66)}{46875}+\frac {1}{25} e^{3 x} ((3 c_2-4 c_1) \cos (4 x)+(3 c_1+4 c_2) \sin (4 x))+c_3 \\ \end{align*}