Internal problem ID [1517]
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 20.
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 }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y+{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 76
dsolve(1*diff(y(x),x$4)+1*diff(y(x),x$3)-2*diff(y(x),x$2)-6*diff(y(x),x)-4*y(x)=-exp(2*x)*(4+28*x+15*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (x^{2}-1\right ) \left (-15 \,{\mathrm e}^{2 x} x^{2}-28 \,{\mathrm e}^{2 x} x -4 \,{\mathrm e}^{2 x}\right )}{90 x^{2}+168 x +24}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \cos \relax (x ) {\mathrm e}^{-x}+c_{4} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 48
DSolve[1*y''''[x]+1*y'''[x]-2*y''[x]-6*y'[x]-4*y[x]==-Exp[2*x]*(4+28*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{90} e^{2 x} \left (-15 x^3+15 x-11+90 c_4\right )+e^{-x} (c_2 \cos (x)+c_1 \sin (x)+c_3) \\ \end{align*}