# solve differential equation dy/dx= 7y^2/sqrtx, y(1)=1/36

y(x)=

1. To solve this differential equation, we can separate the variables:

dy/y^2 = 7/sqrt(x) dx

Integrating both sides:

-1/y = 14*sqrt(x) + C

where C is the constant of integration.

To find the value of C, we can use the initial condition:

-1/1 = 14*sqrt(1) + C
C = -15

Substituting C back into the equation, we get:

-1/y = 14*sqrt(x) - 15

Multiplying both sides by -1 and taking the reciprocal:

y(x) = 1 / (15 - 14*sqrt(x))

Thus, the solution to the differential equation with the initial condition y(1) = 1/36 is:

y(x) = 1 / (15 - 14*sqrt(x))

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