Internal problem ID [1561]
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 64.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y=\left (x +1\right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)*(1+x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (x^{4}+4 x^{3}+\left (24 c_{3} +3\right ) x^{2}+24 c_{2} x +24 c_{1} \right )}{24} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 37
DSolve[y'''[x]-3*y''[x]+3*y'[x]-1*y[x]==Exp[x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^x \left (x^4+4 x^3+24 c_3 x^2+24 c_2 x+24 c_1\right ) \]