Question

Apply the existence & uniqueness theorem to find and draw the region in the ty-plane where...

Apply the existence & uniqueness theorem to find and draw the region in the ty-plane where there exists a unique solution to the following differential equation with initial condition y(t0)=t0

y (1+t3) y' -t 2=1

This is completing question from my professor

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Answer #1

Any doubt in any step then comment below..

So we see that for y not equal to zero ...both f(t,y) and its oartial derivative both are exist and continous...

Therefore we depend on initial value y0...

If that is positive then we take upper half plane ...

If that is negative then we take lower half plane..  

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