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]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y={\mathrm e}^{-x} \left (20-12 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -4, y^{\prime \prime }\left (0\right ) = 7, y^{\prime \prime \prime }\left (0\right ) = -22] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = \left (-x^{3}+2 x^{2}-x +2\right ) {\mathrm e}^{-x}+\cos \left (x \right )-\sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 39
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]
\[ y(x)\to e^{-x} \left (-x^3+2 x^2-x-e^x \sin (x)+e^x \cos (x)+2\right ) \]