Trying to solve a second order ODE

[cahill8]

Homework Statement

I'm trying to solve a second order ODE for $$y(x)$$ to show that the solution is $$y(x)=sin(x)/x$$. We've been told to use the substitution $$y(x)=h(x)/x$$. I've got to the stage of solving for $$h(x)$$, arriving at $$h''(x)=-x$$. Using the general solution, $$h(x)=A sin(x) + B cos(x)$$ and substiting this into the original equation for $$y(x)$$ I get $$y(x)=(A sin(x) + B cos(x))/x$$

So all that's left to do it seems is to use the inital conditions to show A=1 and B=0 however the problem says to use the inital condition $$y(0)=1$$. This doesn't make sense to me since y is singular at x=0. Is this inital condition a mistake or am I missing something?

Homework Equations

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The Attempt at a Solution

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[tiny-tim]

hi cahill8!

lim_x->0 sinx/x = 1