19.27 problem section 9.3, problem 27

Internal problem ID [1524]

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 27.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_y]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-{\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right )=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 56

dsolve(1*diff(y(x),x$4)+3*diff(y(x),x$3)+3*diff(y(x),x$2)+1*diff(y(x),x)-0*y(x)=exp(-x)*(5-24*x+10*x^2),y(x), singsol=all)
 

\[ y \relax (x ) = -\frac {\left (x^{5}-x^{4}+x^{3}+6 x^{2} c_{3}+3 x^{2}+6 c_{2} x +12 x c_{3}+6 x +6 c_{1}+6 c_{2}+12 c_{3}+6\right ) {\mathrm e}^{-x}}{6}+c_{4} \]

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 64

DSolve[1*y''''[x]+3*y'''[x]+3*y''[x]+1*y'[x]-0*y[x]==Exp[-x]*(5-24*x+10*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} e^{-x} \left (-x \left (x^4-x^3+x^2+3 x+6 c_3 (x+2)+6+6 c_2\right )-6 \left (-c_4 e^x+1+c_1+c_2+2 c_3\right )\right ) \\ \end{align*}