Internal problem ID [1569]
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 72.
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 \prime }+2 y^{\prime }+y-{\mathrm e}^{-x} \left (20-12 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = -4, y^{\prime \prime }\relax (0) = 7, y^{\prime \prime \prime }\relax (0) = -22] \end {align*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 31
dsolve([diff(y(x),x$4)+2*diff(y(x),x$3)+2*diff(y(x),x$2)+2*diff(y(x),x)+1*y(x)=exp(-x)*(20-12*x),y(0) = 3, D(y)(0) = -4, (D@@2)(y)(0) = 7, (D@@3)(y)(0) = -22],y(x), singsol=all)
\[ y \relax (x ) = \left (-x^{3}+2 x^{2}-x +2\right ) {\mathrm e}^{-x}+\cos \relax (x )-\sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 27
DSolve[{y''''[x]+2*y'''[x]+2*y''[x]+2*y'[x]+1*y[x]==Exp[-x]*(20-12*x),{y[0]==3,y'[0]==-4,y''[0]==7,y'''[0]==-22}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-x} (x-2) \left (x^2+1\right )-\sin (x)+\cos (x) \\ \end{align*}