Internal problem ID [1523]
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 26.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y-{\mathrm e}^{x} \left (11+12 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 52
dsolve(2*diff(y(x),x$4)-5*diff(y(x),x$3)+3*diff(y(x),x$2)+1*diff(y(x),x)-1*y(x)=exp(x)*(11+12*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \left (x +1\right ) \left (12 x \,{\mathrm e}^{x}+11 \,{\mathrm e}^{x}\right )}{66+72 x}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{x} x +c_{3} x^{2} {\mathrm e}^{x}+c_{4} {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 51
DSolve[2*y''''[x]-5*y'''[x]+3*y''[x]+1*y'[x]-1*y[x]==Exp[x]*(11+12*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{54} e^x \left (3 x \left (3 x \left (x^2+x-2+6 c_4\right )+8+18 c_3\right )-16+54 c_2\right )+c_1 e^{-x/2} \\ \end{align*}