Internal problem ID [13418]
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: 0.0 (sec). Leaf size: 49
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)
\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} -\frac {{\mathrm e}^{2 x} \left (\left (x^{3}-3 x \right ) \cos \left (x \right )+\left (-2 x^{2}+3\right ) \sin \left (x \right )\right ) x}{8} \]
✓ 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]
\[ y(x)\to \frac {1}{16} e^{2 x} \left (2 \left (2 x^3-3 x+8 c_1\right ) \sin (x)+\left (-2 x^4+6 x^2-3+16 c_2\right ) \cos (x)\right ) \]