12.19.69 problem section 9.3, problem 69

Internal problem ID [2216]
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 69
Date solved : Monday, January 27, 2025 at 05:43:40 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x} \left (1-6 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=7\\ y^{\prime \prime }\left (0\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 29

dsolve([diff(y(x),x$3)-2*diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=2*exp(x)*(1-6*x),y(0) = 2, D(y)(0) = 7, (D@@2)(y)(0) = 9],y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{5 x}+x^{2} {\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 27

DSolve[{D[y[x],{x,3}]-2*D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==2*Exp[x]*(1-6*x),{y[0]==2,Derivative[1][y][0] ==7,Derivative[2][y][0] ==9}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x^2+2\right )-e^{-2 x}+e^{3 x} \]