Question

solve: dx/dt +5x-2y=t ; dy/dt +2x+y=t​

Answer 1

Given:

             $\frac{dx}{dt} +5x -2y = t$

             $\frac{dy}{dt} + 2x + y = t$

To Find :

           $\frac{dy}{dx} = ?$

Step-by-step explanation:

   $\frac{dx}{dt} +5x -2y = t$

=  $\frac{dx}{dt} = t +5x + 2y$    &

   $\frac{dy}{dt} + 2x + y = t$

=  $\frac{dy}{dt} = t - 2x - y$

According to partial differentiation, we can differentiate dx & dy w.r.t  t

i.e.   $\frac{dx}{dt} \& \frac{dy}{dt}$

by the rule of derivative,

   $\frac{dy}{dx} = \frac{dy}{dt} * \frac{dt}{dx}$

   $\frac{dy}{dx} =$ ( t-5x+2y) * (t-2x-y)

=  $t^2 + 10x^2 - 2y^2 + yt -xy - 7xt$

∴  $\mathbf{\displaystyle \frac{dy}{dx} = t^2 + 10x^2 - 2y^2 + yt -xy - 7xt}$