12.19.64 problem section 9.3, problem 64

Internal problem ID [2211]
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
Date solved : Monday, January 27, 2025 at 05:43:36 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=\left (1+x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ y = \frac {{\mathrm e}^{x} \left (x^{4}+4 x^{3}+\left (24 c_3 +3\right ) x^{2}+24 c_2 x +24 c_1 \right )}{24} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-1*y[x]==Exp[x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} e^x \left (x^4+4 x^3+24 c_3 x^2+24 c_2 x+24 c_1\right ) \]