Internal problem ID [5401]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y=x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(diff(y(x),x$2)+2*y(x)=x^3+x^2+exp(-2*x)+cos(3*x),y(x), singsol=all)
\[ y = c_{1} \cos \left (\sqrt {2}\, x \right )+c_{2} \sin \left (\sqrt {2}\, x \right )+\frac {{\mathrm e}^{-2 x}}{6}-\frac {\cos \left (3 x \right )}{7}-\frac {1}{2}-\frac {3 x}{2}+\frac {x^{2}}{2}+\frac {x^{3}}{2} \]
✓ Solution by Mathematica
Time used: 4.775 (sec). Leaf size: 69
DSolve[y''[x]+2*y[x]==x^3+x^2+Exp[-2*x]+Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{42} \left (21 x^3+21 x^2-63 x+7 e^{-2 x}+9 \sin (x) \sin (2 x)-6 \cos ^3(x)+42 c_1 \cos \left (\sqrt {2} x\right )+42 c_2 \sin \left (\sqrt {2} x\right )-21\right ) \]