Internal problem ID [1509]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {8 y^{\prime \prime \prime }-12 y^{\prime \prime }+6 y^{\prime }-y-{\mathrm e}^{\frac {x}{2}} \left (4 x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
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)
\[ y \relax (x ) = \left (\frac {1}{192} x^{3}+\frac {1}{256} x^{2}\right ) \left (4 x \,{\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{\frac {x}{2}}\right )+c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} x \,{\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{\frac {x}{2}} x^{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 39
DSolve[8*y'''[x]-12*y''[x]+6*y'[x]-y[x]==Exp[x/2]*(1+4*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}