I have encountered this problem and don't know how to work it out. Anyone willing to explain it to me?
An analysis of the motion of a particle resulted in the differential equation d^2y/dx^2 + b^2y=0
Show that y=asinbx is a solution to the equation.
OK, I'll give it a try but I think I'm destined to fail.....And sorry for not using Latex, I'm still learning...
If the second derivitive is -b^2y then the derivitive may be -b^3y^2/6? and the function may be -b^4y^3/72?
If -b^4y^3/72 then I cannot see how y=asinbx can be a solution.
That's where I'm at.