12.19.62 problem section 9.3, problem 62

Internal problem ID [2209]
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 62
Date solved : Monday, January 27, 2025 at 05:43:35 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 29

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=exp(2*x)*(5-4*x-3*x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 37

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==Exp[2*x]*(5-4*x-3*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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