Internal problem ID [4327]
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]]
\[ \boxed {y^{\prime \prime }+y-2 \sin \left (x \right )-4 x \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+y(x)=2*sin(x)+4*x*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+\sin \left (x \right ) \left (x^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 28
DSolve[y''[x]+y[x]==2*Sin[x]+4*x*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (2 x^2-1+2 c_2\right ) \sin (x)+c_1 \cos (x) \\ \end{align*}