Internal problem ID [1568]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime }-3 y^{\prime }-y-{\mathrm e}^{-\frac {x}{2}} \left (-3 x +2\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1, y^{\prime }\relax (0) = 15, y^{\prime \prime }\relax (0) = -17] \end {align*}
✓ Solution by Maple
Time used: 0.03 (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)
\[ y \relax (x ) = \frac {\left (x^{3}+192 x \right ) {\mathrm e}^{-\frac {x}{2}}}{12}-{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 35
DSolve[{4*y'''[x]-0*y''[x]-3*y'[x]-1*y[x]==Exp[-x/2]*(2-3*x),{y[0]==2,y'[0]==0,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} e^{-x/2} \left (3 x \left (x^2+8\right )+8 e^{3 x/2}+64\right ) \\ \end{align*}