Internal problem ID [1503]
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 6.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-2 y={\mathrm e}^{x} \left (15 x^{2}+34 x +14\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$3)+diff(y(x),x$2)-2*y(x)=exp(x)*(14+34*x+15*x^2),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} \cos \left (x \right )+c_{3} \sin \left (x \right )\right ) {\mathrm e}^{-x}+{\mathrm e}^{x} \left (x^{3}+x^{2}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 49
DSolve[y'''[x]+y''[x]-2*y[x]==Exp[x]*(14+34*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} e^{-x} \left (e^{2 x} \left (5 x^3+5 x^2-2+5 c_3\right )+5 c_2 \cos (x)+5 c_1 \sin (x)\right ) \]