73.15.10 problem 22.4

Internal problem ID [15441]
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 : 22.4
Date solved : Tuesday, January 28, 2025 at 07:55:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 30

dsolve([diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=-4*cos(x)+7*sin(x),y(0) = 8, D(y)(0) = -5],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-2 x} \left (\left (\cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{2 x}+3 \,{\mathrm e}^{7 x}+12\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 30

DSolve[{D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-4*Cos[x]+7*Sin[x],{y[0]==8,Derivative[1][y][0] ==-5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (3 e^{-2 x} \left (e^{7 x}+4\right )-\sin (x)+\cos (x)\right ) \]