73.15.51 problem 22.11 (j)

Internal problem ID [15482]
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 (j)
Date solved : Tuesday, January 28, 2025 at 07:58:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{4 x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=exp(4*x)*sin(2*x),y(x), singsol=all)
 

\[ y = \left (c_{1} \cos \left (4 x \right )+c_{2} \sin \left (4 x \right )\right ) {\mathrm e}^{2 x}-\frac {{\mathrm e}^{4 x} \left (-2 \sin \left (2 x \right )+\cos \left (2 x \right )\right )}{40} \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 90

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+20*y[x]==Exp[4*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\cos (4 x) \int _1^x-\frac {1}{4} e^{2 K[2]} \sin (2 K[2]) \sin (4 K[2])dK[2]+\sin (4 x) \int _1^x\frac {1}{4} e^{2 K[1]} \cos (4 K[1]) \sin (2 K[1])dK[1]+c_2 \cos (4 x)+c_1 \sin (4 x)\right ) \]