12.19.38 problem section 9.3, problem 38

Internal problem ID [2185]
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 38
Date solved : Monday, January 27, 2025 at 05:43:12 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 (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.415 (sec). Leaf size: 41

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(x)*(2*cos(2*x)-sin(2*x)),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_1 +{\mathrm e}^{2 x} c_2 +{\mathrm e}^{x} \left (\frac {\cos \left (x \right )^{2}}{6}+\left (c_3 -\frac {\sin \left (x \right )}{6}\right ) \cos \left (x \right )+c_4 \sin \left (x \right )-\frac {1}{12}\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 56

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[x]*(2*Cos[2*x]-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{-x}+c_4 e^{2 x}+\frac {1}{12} e^x (\cos (2 x)-\sin (2 x))+c_2 e^x \cos (x)+c_1 e^x \sin (x) \]