12.19.55 problem section 9.3, problem 55

Internal problem ID [2202]
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 55
Date solved : Monday, January 27, 2025 at 05:43:29 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+11*diff(y(x),x$2)-14*diff(y(x),x)+10*y(x)=-exp(x)*(sin(x)+2*cos(2*x)),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} \left (\left (6 c_3 +\frac {7}{3}\right ) \cos \left (2 x \right )+\left (x +6 c_4 \right ) \sin \left (2 x \right )+\left (x +6 c_1 \right ) \cos \left (x \right )+6 \left (c_2 +\frac {1}{9}\right ) \sin \left (x \right )\right )}{6} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 53

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+11*D[y[x],{x,2}]-14*D[y[x],x]+10*y[x]==-Exp[x]*(Sin[x]+2*Cos[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{36} e^x ((11+36 c_2) \cos (2 x)+(1+36 c_3) \sin (x)+6 \cos (x) (x+2 (x+6 c_1) \sin (x)+6 c_4)) \]