73.15.73 problem 22.14 (d)

Internal problem ID [15504]
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 : 22.14 (d)
Date solved : Tuesday, January 28, 2025 at 08:00:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=20*sinh(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +5 \,{\mathrm e}^{x}-{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 1.289 (sec). Leaf size: 101

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==20*Sinh[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 \left (5 \left (1-i \tan \left (\frac {x}{2}\right )\right )^{2 i}-\left (1+i \tan \left (\frac {x}{2}\right )\right )^{2 i}\right ) \sinh (x)}{\left (1-i \tan \left (\frac {x}{2}\right )\right )^{2 i}-\left (1+i \tan \left (\frac {x}{2}\right )\right )^{2 i}}+e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \]