15.14.10 problem 10

Internal problem ID [3182]
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 : 10
Date solved : Monday, January 27, 2025 at 07:25:18 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

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

\[ y = \frac {\left (8-17 x +289 c_3 \right ) {\mathrm e}^{4 x}}{289}+\frac {\left (68 x +578 c_{1} +15\right ) \cos \left (x \right )}{578}-\frac {\left (x -34 c_2 +\frac {8}{17}\right ) \sin \left (x \right )}{34} \]

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 52

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

\[ y(x)\to \frac {1}{289} e^{4 x} (-17 x+8+289 c_3)+\left (\frac {2 x}{17}+\frac {13}{1156}+c_1\right ) \cos (x)+\left (-\frac {x}{34}-\frac {21}{289}+c_2\right ) \sin (x) \]