Internal problem ID [1533]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 36.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }+{\mathrm e}^{3 x} \left (\left (-3 x +2\right ) \cos \left (3 x \right )-\left (3 x +3\right ) \sin \left (3 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 94
dsolve(1*diff(y(x),x$3)-6*diff(y(x),x$2)+18*diff(y(x),x)-0*y(x)=-exp(3*x)*((2-3*x)*cos(3*x)-(3+3*x)*sin(3*x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{3 x} \cos \left (3 x \right ) x^{2}}{12}+\frac {11 \cos \left (3 x \right ) {\mathrm e}^{3 x}}{36}-\frac {\sin \left (3 x \right ) {\mathrm e}^{3 x} x}{12}-\frac {37 \sin \left (3 x \right ) {\mathrm e}^{3 x}}{24}+\frac {\cos \left (3 x \right ) {\mathrm e}^{3 x} c_{1}}{6}+\frac {c_{1} \sin \left (3 x \right ) {\mathrm e}^{3 x}}{6}-\frac {c_{2} \cos \left (3 x \right ) {\mathrm e}^{3 x}}{6}+\frac {\sin \left (3 x \right ) {\mathrm e}^{3 x} c_{2}}{6}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.289 (sec). Leaf size: 58
DSolve[1*y'''[x]-6*y''[x]+18*y'[x]-0*y[x]==-Exp[3*x]*((2-3*x)*Cos[3*x]-(3+3*x)*Sin[3*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3-\frac {1}{216} e^{3 x} \left (6 \left (3 x^2+1+6 c_1-6 c_2\right ) \cos (3 x)+\sin (3 x)+18 (x-2 (c_1+c_2)) \sin (3 x)\right ) \\ \end{align*}