12.19.23 problem section 9.3, problem 23

Internal problem ID [2170]
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 23
Date solved : Monday, January 27, 2025 at 05:43:01 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 38

dsolve(1*diff(y(x),x$4)-2*diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=exp(2*x)*(13+33*x+18*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (x^{4}+x^{3}+6 c_4 x +x^{2}+6 c_2 \right ) {\mathrm e}^{2 x}}{6}+{\mathrm e}^{-x} \left (x c_3 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 58

DSolve[1*D[y[x],{x,4}]-2*D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==Exp[2*x]*(13+33*x+18*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{54} e^{2 x} \left (9 x^4+9 x^3+9 x^2+18 (-1+3 c_4) x+10+54 c_3\right )+e^{-x} (c_2 x+c_1) \]