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