Internal problem ID [13767]
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: 22.14 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=5 \sin \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=5*sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} -\frac {\cos \left (2 x \right )}{26}+\frac {1}{2}+\frac {4 \sin \left (2 x \right )}{13} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 45
DSolve[y''[x]-4*y'[x]+5*y[x]==5*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4}{13} \sin (2 x)-\frac {1}{26} \cos (2 x)+c_2 e^{2 x} \cos (x)+c_1 e^{2 x} \sin (x)+\frac {1}{2} \]