Class 12 Differential Equations Solutions has been updated according to the latest syllabus of 2080. It means the notes of applications of differential equations chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of this chapter because we are here to serve you.
Chapter – 15
Differential Equations
A linear differential equation of the first order is an equation that can be written in the standard form:$latex \frac{dy}{dx} + P(x) y = Q(x)$. Here, $latex y$ is the dependent variable, $latex x$ is the independent variable, $latex P(x)$ is a function of $latex x$, and $latex Q(x)$ is also a function of $latex x$.
To solve this type of differential equation, one typically finds an integrating factor, $latex I(x)$, which is given by: $latex I(x) = e^{\int P(x) , dx}$. The solution to the differential equation is then given by: $latex y \cdot I(x) = \int Q(x) \cdot I(x) , dx + C$.
where $latex C$ is the constant of integration. This method is known as the method of integrating factors and is a standard approach to solving first-order linear differential equations.
Class 12 Differential Equations Solutions PDF
This PDF will provide the solutions of every question from the 5th exercise of class 12 differential equations chapter. If you want the notes of other exercises then you can choose the exercise from the button given above.
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Bernoulli’s Equation
Another important topic related to linear differential equations is Bernoulli’s Equation. This is a type of nonlinear differential equation that can be transformed into a linear one by an appropriate substitution.
Bernoulli’s Equation is of the form:$latex \frac{dy}{dx} + P(x) y = Q(x) y^n$, where $latex n$ is any real number.
To solve this equation, it can be converted into a linear differential equation by dividing through by $latex y^n$ and then using the substitution $latex v = y^{1-n}$, which leads to a linear equation in terms of $latex v$. The standard techniques for solving linear differential equations can then be applied.
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