Internal problem ID [1532]
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 35.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y=-{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(1*diff(y(x),x$3)-7*diff(y(x),x$2)+20*diff(y(x),x)-24*y(x)=-exp(2*x)*((13-8*x)*cos(2*x)-(8-4*x)*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-20 x^{2}+40 c_{2} +60 x -83\right ) \cos \left (2 x \right )+20 \sin \left (2 x \right ) \left (x +2 c_{3} -\frac {47}{10}\right )\right ) {\mathrm e}^{2 x}}{40}+c_{1} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.955 (sec). Leaf size: 55
DSolve[1*y'''[x]-7*y''[x]+20*y'[x]-24*y[x]==-Exp[2*x]*((13-8*x)*Cos[2*x]-(8-4*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{40} e^{2 x} \left (\left (-20 x^2+60 x+21+40 c_2\right ) \cos (2 x)+40 c_3 e^x+(20 x-37+40 c_1) \sin (2 x)\right ) \]