A few days ago
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
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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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