Internal problem ID [5390]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=-2 \sin \left (x \right )+4 \cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=-2*sin(x)+4*x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+c_{2} -1\right ) \sin \left (x \right )+2 \cos \left (x \right ) \left (x +\frac {c_{1}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 32
DSolve[y''[x]+y[x]==-2*Sin[x]+4*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (2 x^2-1+2 c_2\right ) \sin (x)+(2 x+c_1) \cos (x) \]