Question

Solve the differential equation y˝ = 6t + sin t, given y´(0) = 0 and y(0) = 5.

Answer 1

Solving this d. e. is pretty straightforward, given that you need only integrate twice with respect to t and to evaluate the constants of integration based on the initial conditions.

Answer 2

In your shoes, I'd write y˝ = 6t + sin t

as \[\frac{ d ^{2}y }{ dt ^{2} }= 6t +\sin t\]

Answer 3

which in turn could be written as \[\frac{ d }{ dt }(\frac{ dy }{ dt }) = 6t + \sin t\]

Answer 4

Multiply every term here by dt, and then integrate the resulting equation with respect to t. Mind trying that?