Internal problem ID [1522]
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 25.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y=\left (x +1\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(1*diff(y(x),x$4)-2*diff(y(x),x$3)-0*diff(y(x),x$2)+2*diff(y(x),x)-1*y(x)=exp(x)*(1+x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{2} +\frac {{\mathrm e}^{x} \left (x^{4}+48 c_{4} x^{2}+2 x^{3}+48 c_{3} x +48 c_{1} \right )}{48} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 55
DSolve[1*y''''[x]-2*y'''[x]-0*y''[x]+2*y'[x]-1*y[x]==Exp[x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{96} e^x \left (2 x^4+4 x^3+(-6+96 c_4) x^2+(6+96 c_3) x-3+96 c_2\right )+c_1 e^{-x} \]