Internal problem ID [1566]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y-2 \,{\mathrm e}^{x} \left (1-6 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 7, y^{\prime \prime }\relax (0) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.029 (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)
\[ y \relax (x ) = \left ({\mathrm e}^{5 x}+x^{2} {\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 27
DSolve[{y'''[x]-2*y''[x]-5*y'[x]+6*y[x]==2*Exp[x]*(1-6*x),{y[0]==2,y'[0]==7,y''[0]==9}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (x^2+2\right )-e^{-2 x}+e^{3 x} \\ \end{align*}