Internal problem ID [1522]
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 25.
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 }-2 y^{\prime \prime \prime }+2 y^{\prime }-y-\left (x +1\right ) {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 47
dsolve(1*diff(y(x),x$4)-2*diff(y(x),x$3)-0*diff(y(x),x$2)+2*diff(y(x),x)-1*y(x)=exp(x)*(1+x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \left (2+x \right ) \left ({\mathrm e}^{x}+x \,{\mathrm e}^{x}\right )}{48 x +48}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{x} x +c_{4} x^{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 49
DSolve[1*y''''[x]-2*y'''[x]-0*y''[x]+2*y'[x]-1*y[x]==Exp[x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+\frac {1}{96} e^x (2 x (x (x (x+2)-3+48 c_4)+3+48 c_3)-3+96 c_2) \\ \end{align*}