Internal problem ID [13425]
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 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(3*x)*sin(2*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}-\frac {{\mathrm e}^{3 x} \left (\left (x^{2}+\frac {16}{5} x -\frac {109}{50}\right ) \cos \left (2 x \right )+2 \sin \left (2 x \right ) \left (x^{2}-\frac {13}{10} x -\frac {22}{25}\right )\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 63
DSolve[y''[x]-5*y'[x]+6*y[x]==x^2*Exp[3*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{500} e^{3 x} \left (2 \left (50 x^2-65 x-44\right ) \sin (2 x)+\left (50 x^2+160 x-109\right ) \cos (2 x)\right )+c_1 e^{2 x}+c_2 e^{3 x} \]