# Differential Equations formula

Differential Equations also called as Partial differential equations if they have partial derivatives. The highest order derivative is the order of differential equation.

## Differential Equation formula

 $\frac{dy}{dt} + p(t)y = g(t)$

p(t) & g(t) are the functions which are continuous.

y(t) = $\frac{\int \mu (t)g(t)dt + c}{\mu (t)}$

Where $\mu (t) = e^{\int p(t)d(t)}$

## Differential Equation formula question

Question 1:

$\frac{dv}{dt}$ = 9.8 – 0.196v, v(0) = 48 , solve this equation.

Solution:

Step 1: Find the general solution:

V = 50 + ce-0.196t>

Step 2: Find the value of c.

48 = v(0) = 50 + c

C = -2

V = 50 – 2e0.196t

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