Internal problem ID [13712]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.7 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{2 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{3 x}+\frac {{\mathrm e}^{2 x} \cos \left (x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 29
DSolve[y''[x]-6*y'[x]+9*y[x]==Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{2 x} \left (\cos (x)+2 e^x (c_2 x+c_1)\right ) \]