Internal problem ID [2243]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=x^{2} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=x^2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{-x} c_{2} +\frac {\left (25 x^{2}+60 x -133\right ) \cos \left (x \right )}{250}+\frac {\sin \left (x \right ) \left (75 x^{2}-170 x +81\right )}{250} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 53
DSolve[y''[x]+3*y'[x]+2*y[x]==x^2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{250} \left (\left (75 x^2-170 x+81\right ) \sin (x)+\left (25 x^2+60 x-133\right ) \cos (x)\right )+c_1 e^{-2 x}+c_2 e^{-x} \]