Internal problem ID [5387]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=x^{2}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=x^2+sin(x),y(x), singsol=all)
\[ y = \cos \left (x \right ) {\mathrm e}^{-x} c_{1} +\sin \left (x \right ) {\mathrm e}^{-x} c_{2} +\frac {x^{2}}{2}-\frac {2 \cos \left (x \right )}{5}+\frac {\sin \left (x \right )}{5}-x +\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 50
DSolve[y''[x]+2*y'[x]+2*y[x]==x^2+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{10} e^{-x} \left (5 e^x (x-1)^2+\left (-4 e^x+10 c_2\right ) \cos (x)+2 \left (e^x+5 c_1\right ) \sin (x)\right ) \]