solve the differential equation
dy / dx = 11x^2y^2
with the condition that y(0) = 4
The solution to the equation is
y =
dy/y^2 = 11x^2 dx
-1/y = 11/3 x^3 + c
Now plug in your initial condition to find c.
i plugged in 11/3 x^3 -1/4 but the answer wasn't correct
To solve the given differential equation, we need to separate the variables and integrate both sides.
First, we can rewrite the given differential equation as:
dy / y^2 = 11x^2 dx
Now, let's integrate both sides:
∫ (dy / y^2) = ∫ (11x^2 dx)
Integrating the left side gives us:
-1 / y = (11/3) x^3 + C1
Where C1 is the constant of integration.
Next, let's solve for y:
y = -1 / ((11/3) x^3 + C1)
Now, we can apply the initial condition y(0) = 4 to find the value of the constant C1.
When x = 0, y = 4:
4 = -1 / (C1)
Multiplying both sides by (C1) gives us:
4C1 = -1
Dividing both sides by 4 gives us:
C1 = -1/4
Substituting the value of C1 back into our equation for y, we get:
y = -1 / ((11/3) x^3 - 1/4)
Therefore, the solution to the given differential equation, with the initial condition y(0) = 4, is:
y = -1 / ((11/3) x^3 - 1/4)