Розвязати
y^2dx=(x+2)dy

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вопрос

To solve this differential equation, we can rearrange the terms to separate the variables:

y^2 dx = (x + 2) dy

Divide both sides by y^2:

dx = (x + 2)/y^2 dy

Now, we can integrate both sides. Integrating the left side with respect to x gives:

∫ dx = x + C1

Integrating the right side with respect to y gives:

∫ (x + 2)/y^2 dy = ∫ (x/y^2 + 2/y^2) dy = x/y + (-2/y) + C2 = x/y - 2/y + C2

Therefore, the general solution to the differential equation is:

x + C1 = x/y - 2/y + C2

or rearranged as:

x + 2/y = C

where C is the constant of integration.