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]]
\[ \boxed {2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y={\mathrm e}^{x} \left (11+12 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
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)
\[ y \left (x \right ) = c_{4} {\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{x} \left (x^{4}+6 c_{3} x^{2}+x^{3}+6 c_{2} x +6 c_{1} \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 58
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]
\[ y(x)\to e^x \left (\frac {x^4}{6}+\frac {x^3}{6}+\left (-\frac {1}{3}+c_4\right ) x^2+\left (\frac {4}{9}+c_3\right ) x-\frac {8}{27}+c_2\right )+c_1 e^{-x/2} \]