12.19.36 problem section 9.3, problem 36

Internal problem ID [2183]
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 36
Date solved : Monday, January 27, 2025 at 05:43:10 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+18 y^{\prime }&=-{\mathrm e}^{3 x} \left (\left (2-3 x \right ) \cos \left (3 x \right )-\left (3+3 x \right ) \sin \left (3 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

dsolve(1*diff(y(x),x$3)-6*diff(y(x),x$2)+18*diff(y(x),x)-0*y(x)=-exp(3*x)*((2-3*x)*cos(3*x)-(3+3*x)*sin(3*x)),y(x), singsol=all)
 

\[ y = \frac {\left (\left (-3 x^{2}+6 c_1 -6 c_2 -1\right ) \cos \left (3 x \right )-3 \left (x -2 c_1 -2 c_2 +\frac {1}{9}\right ) \sin \left (3 x \right )\right ) {\mathrm e}^{3 x}}{36}+c_3 \]

✓ Solution by Mathematica

Time used: 1.526 (sec). Leaf size: 57

DSolve[1*D[y[x],{x,3}]-6*D[y[x],{x,2}]+18*D[y[x],x]-0*y[x]==-Exp[3*x]*((2-3*x)*Cos[3*x]-(3+3*x)*Sin[3*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3-\frac {1}{216} e^{3 x} \left (6 \left (3 x^2+1+6 c_1-6 c_2\right ) \cos (3 x)+(18 x+1-36 c_1-36 c_2) \sin (3 x)\right ) \]