Internal problem ID [4836]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 36.
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: 18
dsolve(diff(y(x),x$2)+y(x)=2*sin(x)+4*x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{2}+c_{2} -1\right ) \sin \left (x \right )+\cos \left (x \right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 28
DSolve[y''[x]+y[x]==2*Sin[x]+4*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (2 x^2-1+2 c_2\right ) \sin (x)+c_1 \cos (x) \]