Internal problem ID [1508]
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 11.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y=2 \,{\mathrm e}^{4 x} \left (13+15 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(x),x$3)-7*diff(y(x),x$2)+8*diff(y(x),x)+16*y(x)=2*exp(4*x)*(13+15*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}+c_{3} x +2 x^{2}+c_{2} \right ) {\mathrm e}^{4 x}+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 42
DSolve[y'''[x]-7*y''[x]+8*y'[x]+16*y[x]==2*Exp[4*x]*(13+15*x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{4 x} \left (x^3+2 x^2+\left (-\frac {4}{5}+c_3\right ) x+\frac {4}{25}+c_2\right )+c_1 e^{-x} \]