A few days ago
Anadar121

Help! I need to find the general solution of dy/dt = (4t^2+y^2)/(ty)?

Help! I need to find the general solution of dy/dt = (4t^2+y^2)/(ty)?

Top 1 Answers
A few days ago
Anonymous

Favorite Answer

Put y = ut.

Then dy/dt = u + t du/dt.

The equation becomes:

u + t du/dt = (4t^2 + u^2t^2) / ut^2

t du/dt = (4t^2 + u^2t^2) / ut^2 – u

= 4 / u + u – u

= 4 / u

du / dt = 4 / ut

u du = 4 dt / t

Integrating:

u^2 / 2 = 4 ln(t) + c

u^2 = 8 ln(t) + c.

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