15.11.17 problem 17

Internal problem ID [3127]
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 : 17
Date solved : Monday, January 27, 2025 at 07:22:31 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

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

\[ y = \frac {\left (40 c_3 -2 \cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{4 x}}{40}+\cos \left (x \right ) c_{1} +c_2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 44

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

\[ y(x)\to c_3 e^{4 x}+\left (-\frac {e^{4 x}}{20}+c_1\right ) \cos (x)+\left (-\frac {e^{4 x}}{40}+c_2\right ) \sin (x) \]