Solution of Initial Value Problem

[DrunkApple]

Homework Statement

Determine the solution of the IVP y' + 4ty = 4t, y(0) = 6

Homework Equations

The Attempt at a Solution

p(t) = 4t
g(t) = 4t

μ(t) = e^{\int4tdt}
= e^{\int p(t)}
= e^{\int4tdt}
= e^{2t^{2}}

is this all I need? because i did
\frac{d}{dt}(y * μ(t)) = p(t) * g(t)
and the professor made a big red X mark on it, so I am confused.

 

[tiny-tim]

Hi DrunkApple!

p(t) = 4t
g(t) = 4t
…
\frac{d}{dt}(y * μ(t)) = p(t) * g(t)

nooo …

you're multiplying the whole equation by e^2t2,

so the RHS should be e^2t2 * g(t), shouldn't it? ​

 

[DrunkApple]

wow...
can't believe i made that mistake...
thank you super hero tim-tim