12.19.61 problem section 9.3, problem 61

Internal problem ID [2208]
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 61
Date solved : Monday, January 27, 2025 at 05:43:34 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)+1*diff(y(x),x$2)-0*diff(y(x),x)-2*y(x)=-exp(3*x)*(9+67*x+17*x^2),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (x^{2}+2 x -2\right ) {\mathrm e}^{4 x}-2 c_1 \,{\mathrm e}^{2 x}-2 c_2 \cos \left (x \right )-2 c_3 \sin \left (x \right )\right ) {\mathrm e}^{-x}}{2} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 49

DSolve[D[y[x],{x,3}]+1*D[y[x],{x,2}]-0*D[y[x],x]-2*y[x]==-Exp[3*x]*(9+67*x+17*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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