Short question about diff Eq. x' = t * cos(t)²

[ManyTimes]

Short question about diff Eq. x' = t * cos(t)²

Hello, it is me again.

Solving the equation:
x' = t * cos(t)²
x = | t * cos(t)² //Mark: | is the integral sign
x = t * sin(t)²

Is this it? No need to derive "T" at all?

 

[arthur ohlsten]

Re: Short question about diff Eq. x' = t * cos(t)²

dx/dt= t cos t^2
dx/dt = cos t^2 [t]
let u=t^2
then du=2t

dx/dt=[cos u *1/2[2t]
dx/dt=1/2 cos u du
x= 1/2 sin u
x=1/2 sin t^2 + C answer

Arthur

 

[ManyTimes]

Re: Short question about diff Eq. x' = t * cos(t)²

Thanks, so in short; had to derive (derivation) T... Alright.