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How can I find the maximal interval of existence for the solution of $\dfrac{dx}{dt}=4x^2$ , $x(0)=5$ including $t=0$ .

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marked as duplicate by Git Gud, Did, egreg, Davide Giraudo, Alex Wertheim Dec 15 '13 at 13:00

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Start by finding the solution. Then see where it is undefined.

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HINT. As Robert Israel said, find the solution first. I suggest you rewrite your equation as dt/dx = .... and the problem becomes much simpler; the solution is ..... I am sure you can continue from here.

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Separate variables by rearranging terms and then integrating; examine the domain, the set of reals on which the function is defined, and assign the longest interval on which the function is defined to the maximal interval for existence for solutions.

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