Internal problem ID [4323]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-8 \sin \left (x \right ) x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+y(x)=8*x*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (x \right )+c_{1} \cos \left (x \right )+2 x \left (-x \cos \left (x \right )+\sin \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==8*x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-2 x^2+1+c_1\right ) \cos (x)+(2 x+c_2) \sin (x) \\ \end{align*}