15.14.29 problem 31

Internal problem ID [3201]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 31
Date solved : Monday, January 27, 2025 at 07:25:54 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

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

\[ y = \frac {\left (\left (-5 x -20 c_{1} -10 c_2 -4\right ) \cos \left (x \right )-10 \sin \left (x \right ) \left (x -c_{1} +2 c_2 +\frac {3}{10}\right )\right ) {\mathrm e}^{-2 x}}{50}+c_3 \]

✓ Solution by Mathematica

Time used: 0.272 (sec). Leaf size: 52

DSolve[D[y[x],{x,3}]+4*D[y[x],{x,2}]+5*D[y[x],x]==Exp[-2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{50} e^{-2 x} (2 (-5 x+1-10 c_1+5 c_2) \sin (x)-(5 x+14+10 c_1+20 c_2) \cos (x))+c_3 \]