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Discover the Path to Mathematical Mastery
An Education That Counts
Substitution methods are processes for transforming a given equation to reveal a particular structure. Substitution is a powerful technique for solving differential equations, particularly for those that cannot be solved using other methods. Bernoulli differential equations, which are a type of nonlinear first-order differential equation, can often be solved using substitution. This technique involves introducing a new variable and function that relates the original variables in a specific way. In this tutorial, we will explore the steps involved in solving differential equations by substitution, with a focus on Bernoulli differential equations.
Some differential equations may require a substation before we can determine how to solve them.
| Homogenous Equations | Bernoulli’ Differential Equtions | Reduction to Separation of Variables |
| \(M(x,y)dx+N(x,y)dy=0\) | \(\displaystyle\frac{dy}{dx}+P(x)y=f(x)y^n\) | \(\displaystyle\frac{dy}{dx}=f(Ax+By+C)\) |
How do we know when a substitution is a good substitution?
Determine the function that satisfies the given differential equation.
Solve the given differential equation by making a strategic substitution.
Solve the given Bernoulli differential equation.
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