Solve the differential equation: (e^x + e^-x)dy/dx = y^2

The given differential equation is: (e^x + e^-x)dy/dx = y^2 To solve this equation, we can use the method of separation of variables. First, we can rearrange the equation as: dy/dx = y^2 / (e^x + e^-x) Now, we can separate the variables by multiplying both sides by the denominator: (e^x + e^-x)dy = y^2 dx Next, we can integrate both sides: ?(e^x + e^-x)dy = ?y^2 dx Using the power rule for integration, we get: (e^x + e^-x)y / 2 = (y^3 / 3) + C where C is the constant of integration. Finally, we can solve for y by multiplying both sides by 2/(e^x + e^-x) and simplifying: y = (3/2) * ((e^x + e^-x) / (Ce^x + Ce^-x + 2))^(1/2) Therefore, the solution to the given differential equation is: y = (3/2) * ((e^x + e^-x) / (Ce^x + Ce^-x + 2))^(1/2) where C is the constant of integration.