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Solve the following differential equation : x² dy + y(x + y) dx = 0
Find the general solution of the following differential equation : dy/dx = e^(x-y) + x²e^(-y)
A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential growth model, the rate of growth of this sample of bacteria is calculated. The differential equation representing the growth of bacteria is given as : dP/dt = kP, where P is the population of bacteria at any time 't'. Based on the above information, answer the following questions :
Find the general solution of the differential equation dy/dx = xy log x log y.
Find the general solution of the differential equation eˣ tan y dx + (1 − eˣ) sec² y dy = 0.
Solve the differential equation : log(dy/dx) = x − y.
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