johann1301h said:Homework Statement
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Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1
The Attempt at a Solution
i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution. How do i find this solution?
I used that ∫y-2dy = ∫1dx to find the first solution.
Is it really a solution? Replace it back into the original equation.johann1301h said:i find one solution: 1/(1-x). But the math book says 1/(1-2x) also is a solution.
johann1301h said:Homework Statement
[/B]
Solve the differenetial equation and find the all solutions through (1, 0).
y'/y^2 = 1
A differential equation is a mathematical equation that relates a function to its derivatives. It is used to model various physical phenomena in fields such as physics, engineering, and economics.
To solve a differential equation, you need to find a function that satisfies the equation. This can be done using various techniques such as separation of variables, substitution, and integrating factors.
Solving differential equations allows us to understand and predict the behavior of complex systems. It is also essential in many fields of science and engineering, including physics, biology, and economics.
The three main types of differential equations are ordinary differential equations, partial differential equations, and stochastic differential equations. Ordinary differential equations involve one independent variable, while partial differential equations involve multiple independent variables. Stochastic differential equations involve randomness or uncertainty in the system.
Differential equations can be used to model and understand various phenomena in the real world, such as population growth, radioactive decay, and the spread of diseases. They are also used in engineering to design and analyze systems, such as electrical circuits and fluid dynamics.