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Because y itself does not appear in that equation, let z= dy/dx so the equation becomes $\displaystyle \frac{dz}{dx}- z^2+ 4= 0$. That's a very simple separable first order equation for z. Since z= dy/dx, integrate to find y.
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$\displaystyle \frac{dz}{dx} = z^2 - 4 = (z-2)(z+2) \Rightarrow \frac{dz}{(z-2)(z+2)} = dx$...
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Originally Posted by dapore Find the solution You can conver this to a first order problem using substitution $\displaystyle u = \frac{dy}{dx} $.
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