Methods of Solving First Order, First Degree Differential Equations - Differential Equations with Variables Separable Method

The solution of the differential equation, ${\displaystyle \frac{dy}{dx}}$ = (x – y)², when y (1) = 1, is ______.

For the differential equation find a particular solution satisfying the given condition:

${\displaystyle \frac{dy}{dx}}$ = y tan x; y = 1 when x = 0

Solve

${\displaystyle y\log y\frac{dy}{dx}+x –\log y=0}$

The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.

The resale value of a machine decreases over a 10 year period at a rate that depends on the age of the machine. When the machine is x years old, the rate at which its value is changing is ₹ 2200 (x − 10) per year. Express the value of the machine as a function of its age and initial value. If the machine was originally worth ₹1,20,000, how much will it be worth when it is 10 years old?

Fill in the blank:

The integrating factor of the differential equation ${\displaystyle \frac{dy}{dx}–y=x}$ is __________

For the differential equation, find the general solution:

sec² x tan y dx + sec² y tan x dy = 0

Find the equation of a curve passing through the point (0, -2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.