12.19.71 problem section 9.3, problem 71

Internal problem ID [2218]
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 71
Date solved : Monday, January 27, 2025 at 05:43:41 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=15\\ y^{\prime \prime }\left (0\right )&=-17 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 22

dsolve([4*diff(y(x),x$3)-0*diff(y(x),x$2)-3*diff(y(x),x)-1*y(x)=exp(-x/2)*(2-3*x),y(0) = -1, D(y)(0) = 15, (D@@2)(y)(0) = -17],y(x), singsol=all)
 

\[ y = \frac {\left (x^{3}+192 x \right ) {\mathrm e}^{-\frac {x}{2}}}{12}-{\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 35

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

\[ y(x)\to \frac {1}{36} e^{-x/2} \left (3 x^3+24 x+8 e^{3 x/2}+64\right ) \]