12.19.41 problem section 9.3, problem 41

Internal problem ID [2188]
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 41
Date solved : Monday, January 27, 2025 at 05:43:13 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

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

\[ y = \frac {{\mathrm e}^{-2 x} \left (10 c_1 \,{\mathrm e}^{3 x}+\left (\left (x +10 c_3 +\frac {14}{5}\right ) \cos \left (x \right )+2 \left (x +5 c_4 -\frac {1}{5}\right ) \sin \left (x \right )\right ) {\mathrm e}^{x}+10 c_2 \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 58

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

\[ y(x)\to \frac {1}{50} e^{-2 x} \left (50 \left (c_4 e^{3 x}+c_3\right )+e^x (5 x+14+50 c_2) \cos (x)+e^x (10 x-7+50 c_1) \sin (x)\right ) \]