15.14.24 problem 24

Internal problem ID [3196]
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 : 24
Date solved : Monday, January 27, 2025 at 07:25:51 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+9*diff(y(x),x$2)=sin(3*x)+x*exp(x),y(x), singsol=all)
 

\[ y = \frac {\left (3 c_{1} x +3 c_2 -2 c_{1} \right ) {\mathrm e}^{3 x}}{27}-\frac {\cos \left (3 x \right )}{162}+\frac {\left (x -1\right ) {\mathrm e}^{x}}{4}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 1.127 (sec). Leaf size: 52

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,3}]+9*D[y[x],{x,2}]==Sin[3*x]+x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^x (x-1)-\frac {1}{162} \cos (3 x)+\frac {1}{27} e^{3 x} (c_2 (3 x-2)+3 c_1)+c_4 x+c_3 \]