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Differential Equations - Definition

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  • "Differential EquationsDefinition: An equation involving one dependent variable and one or more independent variables and thederivatives of dependent variables with respect to independent variable is called a differentialequation.The differential equ..

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  • "Differential EquationsDefinition: An equation involving one dependent variable and one or more independent variables and thederivatives of dependent variables with respect to independent variable is called a differentialequation.The differential equation which contains one independent variable and ordinary derivatives withrespect to this independent variable is said to be an ordinary differential equation.A differential equation is said to be a partial differential equation if it contains at least twoindependent variables and partial derivatives with respect to either of these independentvariables.Importance: The differential equations are used in Physics, Chemistry, Biology, Applied mathematics andmany other fields. Especially differential equations are used in many physical laws involved inthe rate of the physical quantity. Differential equations play an important role in modeling everyphysical, technical or biological process. Differential equations such as those used to solve real- life problems may not necessarily be directly solvable, but we can calculate the approximatesolution.Differential equations can be divided into different types:? Ordinary Differential equations 2 ?? ? ?+ 3 = sin ?2 ? ? ? ? ? Partial Differential equations2 ? ? ? ? + + 4 ? = 22 ? ? ? ? Difficulties and techniques to solve the Differential equation: As there are different methods to solve the given differential equation, it is important to selectthe suitable method. We may use more than one method to solve the single differential equation.The Student who lacks the concepts of differentiation and integration will have to face thedifficulty while solving the question. So the Student needs the concepts of not only thederivatives but also the integration methods though the name indicates solving the differentialequation.We can solve the given differential equation by using different methods:Variables separable method: By separating the derivatives of the different variables andintegrate them separately solve the equation.? ? ? ( ? , ? ) Homogeneous method: For the equation= , if the functions are of same degree in x? ? ? ( ? , ? ) and y then the equation is said to be homogeneous differential equation. By substituting one variable in terms of other variable and then apply variable separable method to solve theequation.Advantages: Our portal is the best online resource of many Students across the world. The Student can accessour online portal and utilize the services of our experts 24 x 7. There will be no time constraintso that the Student will be able to fulfill their needs at the right time. We have the greateststrength of experts proficient in their own domain and ready to help you anytime. We help you tocomplete your project with high standards and great quality. The information provided by usincludes the basics of the concept, importance and also various applications. It helps you tounderstand the topic thoroughly and gain in depth knowledge. "

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