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]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=\cos \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=x^2*cos(x),y(x), singsol=all)
\[ y = -c_{1} {\mathrm e}^{-2 x}+\frac {\cos \left (x \right ) x^{2}}{10}-\frac {133 \cos \left (x \right )}{250}+\frac {3 x^{2} \sin \left (x \right )}{10}-\frac {17 x \sin \left (x \right )}{25}+\frac {81 \sin \left (x \right )}{250}+\frac {6 x \cos \left (x \right )}{25}+{\mathrm e}^{-x} c_{2} \]
✓ 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]
\[ y(x)\to \frac {1}{250} \left (\left (75 x^2-170 x+81\right ) \sin (x)+\left (25 x^2+60 x-133\right ) \cos (x)\right )+c_1 e^{-2 x}+c_2 e^{-x} \]