Internal problem ID [2829]
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 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime }=\sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+25*diff(y(x),x)=sin(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \,{\mathrm e}^{3 x} \cos \left (4 x \right ) c_{1}}{25}+\frac {4 c_{1} {\mathrm e}^{3 x} \sin \left (4 x \right )}{25}-\frac {4 c_{2} {\mathrm e}^{3 x} \cos \left (4 x \right )}{25}+\frac {3 \,{\mathrm e}^{3 x} \sin \left (4 x \right ) c_{2}}{25}+\frac {2 \sin \left (4 x \right )}{219}-\frac {\cos \left (4 x \right )}{292}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.686 (sec). Leaf size: 60
DSolve[y'''[x]-6*y''[x]+25*y'[x]==Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\left (25+292 (4 c_1-3 c_2) e^{3 x}\right ) \cos (4 x)}{7300}+\frac {\left (50+219 (3 c_1+4 c_2) e^{3 x}\right ) \sin (4 x)}{5475}+c_3 \]