Internal problem ID [11785]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 11.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y=5 \sin \left (2 x \right )+10 x^{2}+3 x +7} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve(diff(y(x),x$3)+diff(y(x),x$2)+3*diff(y(x),x)-5*y(x)=5*sin(2*x)+10*x^2+3*x+7,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (17 c_{3} {\mathrm e}^{-x}-9\right ) \sin \left (2 x \right )}{17}+c_{2} {\mathrm e}^{-x} \cos \left (2 x \right )-2 x^{2}+c_{1} {\mathrm e}^{x}-3 x +\frac {2 \cos \left (2 x \right )}{17}-4 \]
✓ Solution by Mathematica
Time used: 0.419 (sec). Leaf size: 55
DSolve[y'''[x]+y''[x]+3*y'[x]-5*y[x]==5*Sin[2*x]+10*x^2+3*x+7,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x^2-3 x+c_3 e^x+\left (\frac {2}{17}+c_2 e^{-x}\right ) \cos (2 x)+\left (-\frac {9}{17}+c_1 e^{-x}\right ) \sin (2 x)-4 \]