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![Find the solution \( y(t) \) of the initial value problem
\[
t y^{2} y^{\prime}-3 y^{3}-6 t^{3}=0, \quad y(1)=2
\]](https://media.cheggcdn.com/media/86d/86d3d4b1-ebc9-40a3-b2cf-b327e418b294/phpPNd2xd)
Expert Answer
Given that,ty2y??3y3?6t3=0?y2y??3y3t=6t2……..(1)let us consider y3=zthen 3y2y?=z??y2y?=13z?Putting these values in (1) we get,13z??3zt=6t2?z??9zt=18t2