Internal problem ID [11791]
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: 17.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=2 x^{2}+4 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(diff(y(x),x$3)+diff(y(x),x)=2*x^2+4*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-2-c_{2} \right ) \cos \left (x \right )+\left (-2 x +c_{1} \right ) \sin \left (x \right )+\frac {2 x^{3}}{3}-4 x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.233 (sec). Leaf size: 35
DSolve[y'''[x]+y'[x]==2*x^2+4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 x^3}{3}-4 x-(2+c_2) \cos (x)+(-2 x+c_1) \sin (x)+c_3 \]