12.19.12 problem section 9.3, problem 12

Internal problem ID [2159]
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 12
Date solved : Monday, January 27, 2025 at 05:42:55 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y&={\mathrm e}^{\frac {x}{2}} \left (1+4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 33

dsolve(8*diff(y(x),x$3)-12*diff(y(x),x$2)+6*diff(y(x),x)-y(x)=exp(x/2)*(1+4*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {x}{2}} \left (x^{4}+x^{3}+\left (48 c_3 +\frac {3}{16}\right ) x^{2}+48 c_2 x +48 c_1 \right )}{48} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 39

DSolve[8*D[y[x],{x,3}]-12*D[y[x],{x,2}]+6*D[y[x],x]-y[x]==Exp[x/2]*(1+4*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{48} e^{x/2} \left (x^4+x^3+48 c_3 x^2+48 c_2 x+48 c_1\right ) \]