12.19.47 problem section 9.3, problem 47

Internal problem ID [2194]
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 47
Date solved : Monday, January 27, 2025 at 05:43:21 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 44

dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+26*diff(y(x),x$2)-40*diff(y(x),x)+25*y(x)=exp(2*x)*(3*cos(1*x)-(1+3*x)*sin(1*x)),y(x), singsol=all)
 

\[ y = \frac {\left (\left (x^{3}+x^{2}+\left (8 c_4 +3\right ) x +8 c_2 -2\right ) \sin \left (x \right )+8 \left (\left (c_3 +\frac {1}{4}\right ) x +c_1 +\frac {9}{16}\right ) \cos \left (x \right )\right ) {\mathrm e}^{2 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 60

DSolve[1*D[y[x],{x,4}]-8*D[y[x],{x,3}]+26*D[y[x],{x,2}]-40*D[y[x],x]+25*y[x]==Exp[2*x]*(3*Cos[1*x]-(1+3*x)*Sin[1*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{16} e^{2 x} \left (\left (2 x^3+2 x^2+(9+16 c_2) x-1+16 c_1\right ) \sin (x)+(2 (1+8 c_4) x+3+16 c_3) \cos (x)\right ) \]