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It's very difficult to read your images.hotjohn said:
Which part of the working that you can't read?SammyS said:
None of it is easy to read.hotjohn said:
SammyS said:
The equation "Dy/dx + (y/x) = x(y^3)" is a first-order linear differential equation.
To solve the equation "Dy/dx + (y/x) = x(y^3)", you can use the method of integrating factors. First, rearrange the equation to the form dy/dx + P(x)y = Q(x), where P(x) = 1/x and Q(x) = x(y^3). Then, multiply both sides by the integrating factor μ(x) = e^(∫P(x)dx), which in this case is μ(x) = e^(∫1/x dx) = e^lnx = x. This gives the equation x(dy/dx) + (xy/x) = x^2(y^3). The left side can now be simplified to d(xy)/dx, and the right side can be integrated with respect to x. Finally, solve for y to get the general solution.
No, the equation "Dy/dx + (y/x) = x(y^3)" cannot be solved with separation of variables because it is not in the form dy/dx = f(x)g(y). Instead, it is a first-order linear differential equation, which requires the method of integrating factors to solve.
The solution to the equation "Dy/dx + (y/x) = x(y^3)" is y = (c + 1/x^2)^(1/3), where c is a constant. This is the general solution obtained through the method of integrating factors.
The equation "Dy/dx + (y/x) = x(y^3)" is a first-order linear differential equation, which is a fundamental concept in differential equations and is used to model many real-world phenomena in various fields of science and engineering. Solving this equation allows us to understand and predict how certain variables change over time, which is crucial in making important decisions and advancements in our understanding of the world.
