Internal problem ID [1500]
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 3.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y=-{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(4*diff(y(x),x$3)+8*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=-exp(x)*(4+45*x+6*x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-18 x^{2} {\mathrm e}^{3 x}-27 x \,{\mathrm e}^{3 x}+149 \,{\mathrm e}^{3 x}+27 c_{3} {\mathrm e}^{\frac {5 x}{2}}+27 c_{2} {\mathrm e}^{\frac {3 x}{2}}+27 c_{1} \right ) {\mathrm e}^{-2 x}}{27} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[4*y'''[x]+8*y''[x]-y'[x]-2*y[x]==-Exp[x]*(4+45*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-\frac {2 x^2}{3}-x+\frac {149}{27}\right )+c_1 e^{-x/2}+c_2 e^{x/2}+c_3 e^{-2 x} \]