Internal problem ID [13424]
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: 22.11 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*cos(2*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+\frac {\left (676 x^{2}-2080 x -1909\right ) \cos \left (2 x \right )}{35152}+\frac {\left (-3380 x^{2}-3796 x -725\right ) \sin \left (2 x \right )}{35152} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 58
DSolve[y''[x]-5*y'[x]+6*y[x]==x^2*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (676 x^2-2080 x-1909\right ) \cos (2 x)-\left (3380 x^2+3796 x+725\right ) \sin (2 x)}{35152}+c_1 e^{2 x}+c_2 e^{3 x} \]