Internal problem ID [1525]
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 28.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(1*diff(y(x),x$4)-7*diff(y(x),x$3)+18*diff(y(x),x$2)-20*diff(y(x),x)+8*y(x)=exp(2*x)*(3-8*x-5*x^2),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (\left (x^{5}-x^{4}-12 c_{4} x^{2}-2 x^{3}-12 c_{3} x -12 c_{2} \right ) {\mathrm e}^{x}-12 c_{1} \right )}{12} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 59
DSolve[1*y''''[x]-7*y'''[x]+18*y''[x]-20*y'[x]+8*y[x]==Exp[2*x]*(3-8*x-5*x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} e^{2 x} \left (-x^5+x^4+2 x^3+6 (-1+2 c_4) x^2+12 (1+c_3) x+12 (-1+c_2)\right )+c_1 e^x \]