12.19.42 problem section 9.3, problem 42

Internal problem ID [2189]
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 42
Date solved : Monday, January 27, 2025 at 05:43:15 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y&={\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 48

dsolve(1*diff(y(x),x$4)-5*diff(y(x),x$3)+13*diff(y(x),x$2)-19*diff(y(x),x)+10*y(x)=exp(x)*(cos(2*x)+sin(2*x)),y(x), singsol=all)
 

\[ y = \frac {3 \,{\mathrm e}^{x} \left (x +\frac {40 c_3}{3}+\frac {1}{15}\right ) \cos \left (2 x \right )}{40}-\frac {{\mathrm e}^{x} \left (x -40 c_4 +\frac {39}{10}\right ) \sin \left (2 x \right )}{40}+{\mathrm e}^{2 x} c_2 +\frac {{\mathrm e}^{x} \left (8 c_1 +1\right )}{8} \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 53

DSolve[1*D[y[x],{x,4}]-5*D[y[x],{x,3}]+13*D[y[x],{x,2}]-19*D[y[x],x]+10*y[x]==Exp[x]*(Cos[2*x]+Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{400} e^x \left (400 \left (c_4 e^x+c_3\right )+(30 x-13+400 c_2) \cos (2 x)-2 (5 x+17-200 c_1) \sin (2 x)\right ) \]