12.19.70 problem section 9.3, problem 70

Internal problem ID [2217]
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 70
Date solved : Monday, January 27, 2025 at 05:43:41 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{-x} \left (4-8 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 23

dsolve([diff(y(x),x$3)-1*diff(y(x),x$2)-1*diff(y(x),x)+1*y(x)=-exp(-x)*(4-8*x),y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
 

\[ y = \left (x^{2}+x +1\right ) {\mathrm e}^{-x}-\left (x -1\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 27

DSolve[{D[y[x],{x,3}]-1*D[y[x],{x,2}]-1*D[y[x],x]+1*y[x]==-Exp[-x]*(4-8*x),{y[0]==2,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (x^2+x-e^{2 x} (x-1)+1\right ) \]