Internal problem ID [2225]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }=\sin \left (3 x \right )+x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {\left (3 c_{1} x -2 c_{1} +3 c_{2} \right ) {\mathrm e}^{3 x}}{27}-\frac {\cos \left (3 x \right )}{162}+\frac {\left (x -1\right ) {\mathrm e}^{x}}{4}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 1.069 (sec). Leaf size: 52
DSolve[y''''[x]-6*y'''[x]+9*y''[x]==Sin[3*x]+x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^x (x-1)-\frac {1}{162} \cos (3 x)+\frac {1}{27} e^{3 x} (c_2 (3 x-2)+3 c_1)+c_4 x+c_3 \]