Internal problem ID [1519]
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 22.
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 }-5 y^{\prime \prime }+4 y-{\mathrm e}^{x} \left (-3 x^{2}+x +3\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 63
dsolve(1*diff(y(x),x$4)+0*diff(y(x),x$3)-5*diff(y(x),x$2)-0*diff(y(x),x)+4*y(x)=exp(x)*(3+x-3*x^2),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (x^{2}+1\right ) \left (-3 x^{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x}+3 \,{\mathrm e}^{x}\right )}{6 \left (3 x^{2}-x -3\right )}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.08 (sec). Leaf size: 50
DSolve[1*y''''[x]+0*y'''[x]-5*y''[x]-0*y'[x]+4*y[x]==Exp[x]*(3+x-3*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} e^x \left (6 \left (x^3+x\right )+7+36 c_3\right )+c_1 e^{-2 x}+c_2 e^{-x}+c_4 e^{2 x} \\ \end{align*}