Squizzel said:Homework Statement
xy^2 dy/dx = y^3 - x^3 , y(1) = 2
Homework Equations
The Attempt at a Solution
It says to solve the initial value problem. I am assuming it is not a Bernoulli, but I can't seem to separate it. What should I do?
Thanks
This is what I get when I separate it, is this right?
y^2-y^3 dy = -x^2 dx
How do you get that last line?Squizzel said:Homework Statement
xy^2 dy/dx = y^3 - x^3 , y(1) = 2
Homework Equations
The Attempt at a Solution
It says to solve the initial value problem. I am assuming it is not a Bernoulli, but I can't seem to separate it. What should I do?
Thanks
This is what I get when I separate it, is this right?
y^2-y^3 dy = -x^2 dx
A separable differential equation is one in which the dependent variable and independent variable can be separated on opposite sides of the equation. A Bernoulli differential equation is a non-linear differential equation that can be transformed into a linear differential equation by using a substitution or transformation.
To determine if a problem is a separable differential equation, check if the equation can be separated into two functions, one with only the dependent variable and the other with only the independent variable. If this is possible, then it is a separable differential equation. To determine if it is a Bernoulli differential equation, check if it is a non-linear equation that can be transformed into a linear equation by using a substitution or transformation.
Separable differential equations are commonly used to model population growth, radioactive decay, and other physical phenomena. Bernoulli differential equations are used in economics, biology, and physics to model various systems, including population dynamics, chemical reactions, and fluid flow.
No, a differential equation can only be one or the other. However, a separable differential equation can sometimes be transformed into a Bernoulli differential equation through a change of variables.
The most common technique for solving a separable differential equation is separation of variables, which involves isolating the dependent and independent variables on opposite sides of the equation. For Bernoulli differential equations, a substitution or transformation can be used to convert the equation into a linear differential equation, which can then be solved using various methods, such as integrating factors or exact equations.