# School's out! Exams are over! Enjoy this problem!

Calculus Level 5

The general solution of the differential equation $$({ y }^{ 2 }+2{ t }^{ 2 }y)dt+(2{ t }^{ 3 }-ty)dy=0$$ is of the form: $$a(ty)^{ { c }/{ d } }-\dfrac { e }{ f } \left(\dfrac { y }{ t } \right)^{ { g }/{ h } }=A$$, where $$A$$ is an arbitrary constant and $$a,c,d,e,f,g,h$$ are all natural numbers, $$a$$ is not divisible by 3, and $$a + e < 14.$$

Find $$a+d+e+f+g+h$$.

Note: c,d are coprime,
e, f are prime,
g, h are coprime.

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