12.19.3 problem section 9.3, problem 3

Internal problem ID [2150]
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 3
Date solved : Monday, January 27, 2025 at 05:42:51 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{x} \left (6 x^{2}+45 x +4\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 50

dsolve(4*diff(y(x),x$3)+8*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=-exp(x)*(4+45*x+6*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (-18 x^{2} {\mathrm e}^{3 x}-27 x \,{\mathrm e}^{3 x}+149 \,{\mathrm e}^{3 x}+27 \,{\mathrm e}^{\frac {5 x}{2}} c_3 +27 c_2 \,{\mathrm e}^{\frac {3 x}{2}}+27 c_1 \right ) {\mathrm e}^{-2 x}}{27} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 52

DSolve[4*D[y[x],{x,3}]+8*D[y[x],{x,2}]-D[y[x],x]-2*y[x]==-Exp[x]*(4+45*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (-\frac {2 x^2}{3}-x+\frac {149}{27}\right )+c_1 e^{-x/2}+c_2 e^{x/2}+c_3 e^{-2 x} \]