12.19.32 problem section 9.3, problem 32

Internal problem ID [2179]
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 32
Date solved : Monday, January 27, 2025 at 05:43:05 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=-{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 48

dsolve(1*diff(y(x),x$3)-2*diff(y(x),x$2)+1*diff(y(x),x)-2*y(x)=-exp(x)*((9+5*x+4*x^2)*cos(2*x)-(6-5*x-3*x^2)*sin(2*x)),y(x), singsol=all)
 

\[ y = \frac {\left (x^{2}+\frac {3}{5} x -\frac {27}{25}\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{2}+\frac {\left (55 x +61\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{50}+\cos \left (x \right ) c_1 +c_2 \sin \left (x \right )+c_3 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 65

DSolve[1*D[y[x],{x,3}]-2*D[y[x],{x,2}]+1*D[y[x],x]-2*y[x]==Exp[2*x]*((9+5*x+4*x^2)*Cos[2*x]-(6-5*x-3*x^2)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{2 x} \left (\left (6760 x^2-17680 x-29907\right ) \sin (2 x)+2 \left (5915 x^2+7345 x+3928\right ) \cos (2 x)\right )}{43940}+c_3 e^{2 x}+c_1 \cos (x)+c_2 \sin (x) \]