15.11.26 problem 26

Internal problem ID [3136]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 26
Date solved : Monday, January 27, 2025 at 07:23:07 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 50

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

\[ y = \left (\cos \left (x \right ) c_3 +c_4 \sin \left (x \right )\right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \left (24 \cos \left (3 x \right )-23 \sin \left (3 x \right )\right )}{1105}+{\mathrm e}^{x} \left (\cos \left (x \right ) c_{1} +c_2 \sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 64

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

\[ y(x)\to \frac {e^{2 x} (24 \cos (3 x)-23 \sin (3 x))}{1105}+c_1 e^{-x} \cos (x)+c_4 e^x \cos (x)+c_2 e^{-x} \sin (x)+c_3 e^x \sin (x) \]