Internal problem ID [13510]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-12 y^{\prime }+36 y=25 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=25*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{6 x} c_{2} +{\mathrm e}^{6 x} x c_{1} +\frac {4 \cos \left (3 x \right )}{9}+\frac {\sin \left (3 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 35
DSolve[y''[x]-12*y'[x]+36*y[x]==25*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \sin (3 x)+\frac {4}{9} \cos (3 x)+e^{6 x} (c_2 x+c_1) \]