Differential Equation Help!

https://isaacphysics.org/questions/maths_ch7_3_q3?board=cbecec52-da2e-46db-90b9-62702dcdf04c&stage=a_level
I am struggling a little with part d
I have d(theta)/d(t)=-I*theta
then separated the variables and did
integral of (1/theta)with respect to d(theta)=integral of (-I)with respect to d(t)
but I am not sure where to go from here
I guess ln(theta)=-It+c, but then how do i include theta_0
Thank you so much!

Original post by MayaVellichor

https://isaacphysics.org/questions/maths_ch7_3_q3?board=cbecec52-da2e-46db-90b9-62702dcdf04c&stage=a_level
I am struggling a little with part d
I have d(theta)/d(t)=-I*theta
then separated the variables and did
integral of (1/theta)with respect to d(theta)=integral of (-I)with respect to d(t)
but I am not sure where to go from here
I guess ln(theta)=-It+c, but then how do i include theta_0
Thank you so much!

When t=0 we have theta=theta_0 so thats how it comes in …. You determine c in terms of it.