y’=7/x³
The given equation is a differential equation which can be written as:
dy/dx = 7/x³
To solve this equation, we need to find the function y(x) that satisfies it
The given equation is a differential equation which can be written as:
dy/dx = 7/x³
To solve this equation, we need to find the function y(x) that satisfies it. Since it is a separable differential equation, we will separate the variables and integrate both sides.
First, let’s rewrite the equation in terms of differentials:
dy = (7/x³)dx
Now, let’s integrate both sides:
∫dy = ∫(7/x³)dx
The integral of dy is simply y, and the integral of (7/x³)dx can be evaluated using the power rule of integration. According to the power rule, the integral of xⁿ dx is (1/(n+1))xⁿ⁺¹ + C, where C is the constant of integration.
Integrating both sides, we get:
y = ∫(7/x³)dx = 7 ∫x⁻³ dx = 7(-1/2)x⁻² + C
Simplifying further, we have:
y = -7/(2x²) + C
So, the general solution to the given differential equation is:
y(x) = -7/(2x²) + C
Here, C represents an arbitrary constant which can be determined if an initial condition or boundary condition is provided.
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