Internal problem ID [1531]
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 34.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+2 y={\mathrm e}^{x} \left (\left (20+4 x \right ) \cos \left (x \right )-\left (12 x +12\right ) \sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+0*diff(y(x),x)+2*y(x)=exp(x)*((20+4*x)*cos(x)-(12+12*x)*sin(x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +{\mathrm e}^{x} \left (\left (x^{2}+x +c_{2} +\frac {22}{5}\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x^{2}+3 x +\frac {1}{5}+c_{3} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 60
DSolve[1*y'''[x]-1*y''[x]+0*y'[x]+2*y[x]==Exp[x]*((20+4*x)*Cos[x]-(12+12*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} e^x \left (10 x^2+10 x+23+10 c_2\right ) \cos (x)+\frac {1}{10} e^x \left (10 x^2+30 x-21+10 c_1\right ) \sin (x)+c_3 e^{-x} \]