15.14.30 problem 32

Internal problem ID [3202]
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 : 32
Date solved : Monday, January 27, 2025 at 07:25:56 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 38

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

\[ y = \frac {\left (104 c_{1} {\mathrm e}^{3 x}+104 c_3 \,{\mathrm e}^{2 x}+\sin \left (2 x \right )+5 \cos \left (2 x \right )-52 c_2 \right ) {\mathrm e}^{-2 x}}{104} \]

✓ Solution by Mathematica

Time used: 0.813 (sec). Leaf size: 42

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

\[ y(x)\to \frac {1}{104} e^{-2 x} \left (\sin (2 x)+5 \cos (2 x)-52 \left (c_1-2 c_2 e^{3 x}\right )\right )+c_3 \]