15.14.11 problem 11

Internal problem ID [3183]
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 : 11
Date solved : Monday, January 27, 2025 at 07:25:19 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 45

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

\[ y = \frac {\left (-3+25 c_2 \right ) \cos \left (2 x \right )}{25}+\frac {\left (-3 x +20 c_4 \right ) \sin \left (2 x \right )}{20}+c_3 \,{\mathrm e}^{-x}+\frac {2 \,{\mathrm e}^{x} \left (x +\frac {5 c_{1}}{2}-\frac {9}{10}\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 55

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

\[ y(x)\to \frac {2 e^x x}{5}-\frac {9 e^x}{25}-\frac {\cos (x)}{2}+c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]