Plus Two Maths Notes Chapter 9 Differential Equations is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 9 Differential Equations.
|Text Book||NCERT Based|
|Chapter Name||Differential Equations|
|Category||Plus Two Kerala|
Kerala Plus Two Maths Notes Chapter 9 Differential Equations
Basic Concepts: order and Degree
- order of a differential equation is the order of the highest order derivative occurring in the differential equation.
- The degree of a differential equation is the highest power (positive integer only) of the highest order derivative in it, after it is made free from radicals and fractions or quotients.
- The degree is defined in the given differential equation is a polynomial equation in its derivatives.
Methods of Solving Differential Equation
I. Variable separable form: An equation in the form M dx + N dy = o. where M = f(x) and N = g (y).
- General solution is ∫ Mdx+ ∫ Ndv = C
II. Homogeneous differential equations: An equation of the form = where f(x,y) and g (x.y) are homogeneous functions of the same degree in x and y.
is also homogeneous.
In order to solve it. put y = vx
After simplification, the given equation
reduces to variable separable form.
- If we are given an equation of the form It is also homogeneous. Here put x = vy then = .
III. Linear differential equations: An equation
in the form +Py = Q, where P, Q are constants or functions of x only
an equation in the form +p1 x = Q,
where P1 and Q1 are constants or functions of y only.
- I. OR
- General solution is
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