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Solving Differential Equations by Variables Separable Method Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Solving Differential Equations by Variables Separable Method Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the variables separable method for solving differential equations?
Ans. The variables separable method is a technique used to solve differential equations by separating the variables on each side of the equation. This involves rearranging the equation so that all terms involving the dependent variable are on one side and all terms involving the independent variable are on the other side. Then, integrating both sides with respect to their respective variables produces the solution.
2. How do you determine if a differential equation is variables separable?
Ans. To determine if a differential equation is variables separable, you need to check if the equation can be rearranged such that all terms involving the dependent variable are on one side and all terms involving the independent variable are on the other side. If this separation is possible, then the equation is variables separable.
3. Can you provide an example of solving a differential equation using the variables separable method?
Ans. Sure! Let's consider the differential equation: dy/dx = x^2 y. To solve this using the variables separable method, we can rearrange the equation as (1/y) dy = x^2 dx. Integrating both sides gives ∫(1/y) dy = ∫x^2 dx, which simplifies to ln|y| = (1/3)x^3 + C, where C is the constant of integration. Finally, we exponentiate both sides to get the solution y = Ce^(x^3/3), where C is an arbitrary constant.
4. Is the variables separable method applicable to all types of differential equations?
Ans. No, the variables separable method is not applicable to all types of differential equations. It can only be used for first-order ordinary differential equations that can be rearranged to separate the variables. Higher-order differential equations or equations with nonlinear terms may require different methods for solving.
5. Are there any limitations or challenges associated with the variables separable method?
Ans. Yes, there are some limitations and challenges associated with the variables separable method. One limitation is that it can only be used for first-order differential equations. Additionally, if the equation cannot be easily rearranged to separate the variables, the method may not be applicable. Furthermore, some equations may require additional algebraic manipulations or substitutions before applying the variables separable method.
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