Internal problem ID [13414]
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: 22.10 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y={\mathrm e}^{2 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+9*y(x)=exp(2*x)*sin(x),y(x), singsol=all)
\[ y = c_{2} \sin \left (3 x \right )+c_{1} \cos \left (3 x \right )-\frac {\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) {\mathrm e}^{2 x}}{40} \]
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 42
DSolve[y''[x]+9*y[x]==Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3}{40} e^{2 x} \sin (x)-\frac {1}{40} e^{2 x} \cos (x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]