# Verify that  `y = -tcos(t) - t` is a solution of the initial value problem  `t(dy/dt) = y + t^2sin(t)` ` ` `y(pi) = 0`

Tibor Pejić | Certified Educator

calendarEducator since 2012

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First we need to find derivative

`dy/dt=-cos t+tsin t-1`

Here we've used product rule to differentiate `-tcos t.`

Now we insert `dy/dt`  and `y` into the initial value problem.

`t(-cos t+tsin t-1)=-tcos...

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