12.19.68 problem section 9.3, problem 68

Internal problem ID [2215]
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 68
Date solved : Monday, January 27, 2025 at 05:43:38 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 46

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+14*diff(y(x),x$2)-20*diff(y(x),x)+25*y(x)=exp(x)*((2+6*x)*cos(2*x)+3*sin(2*x)),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{x} \left (\left (x^{3}+x^{2}+\left (-16 c_3 +\frac {63}{2}\right ) x -16 c_1 -\frac {41}{4}\right ) \cos \left (2 x \right )-16 \left (\left (c_4 +\frac {1}{32}\right ) x +c_2 +\frac {1111}{192}\right ) \sin \left (2 x \right )\right )}{16} \]

✓ Solution by Mathematica

Time used: 0.301 (sec). Leaf size: 62

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+14*D[y[x],{x,2}]-20*D[y[x],x]+25*y[x]==Exp[x]*((2+6*x)*Cos[2*x]+3*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{256} e^x \left (\left (-16 x^3-16 x^2+(6+256 c_4) x+6+256 c_3\right ) \cos (2 x)+(8 (3+32 c_2) x+3+256 c_1) \sin (2 x)\right ) \]