15.43 problem 22.11 (b)

Internal problem ID [13738]

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 (b).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=x^{3} {\mathrm e}^{2 x} \sin \left (x \right )} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=x^3*exp(2*x)*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {{\mathrm e}^{2 x} \left (\left (x^{4}-3 x^{2}-8 c_{1} \right ) \cos \left (x \right )-2 \left (x^{3}-\frac {3}{2} x +4 c_{2} \right ) \sin \left (x \right )\right )}{8} \]

Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 51

DSolve[y''[x]-4*y'[x]+5*y[x]==x^3*Exp[2*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{2 x} \left (2 \left (2 x^3-3 x+8 c_1\right ) \sin (x)+\left (-2 x^4+6 x^2-3+16 c_2\right ) \cos (x)\right ) \]