Internal problem ID [1536]
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 39.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+15 y-{\mathrm e}^{2 x} \left (15 x \cos \left (2 x \right )+32 \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 41
dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+24*diff(y(x),x$2)-32*diff(y(x),x)+15*y(x)=exp(2*x)*(15*x*cos(2*x)+32*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = x \cos \left (2 x \right ) {\mathrm e}^{2 x}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{3 x}+c_{3} \cos \relax (x ) {\mathrm e}^{2 x}+c_{4} \sin \relax (x ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 41
DSolve[1*y''''[x]-8*y'''[x]+24*y''[x]-32*y'[x]+15*y[x]==Exp[2*x]*(15*x*Cos[2*x]+32*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (c_4 e^{2 x}+e^x (x \cos (2 x)+c_2 \cos (x)+c_1 \sin (x))+c_3\right ) \\ \end{align*}