Solving a Differential Equation | dy/dx = 7/x³

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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