There is Exact method differential equations that can make the technique much easier.
Now, if there is a function somewhere out there in the world, Ψ(x,y) Ψ ( x, y), so that, Ψx = M (x,y) and Ψy = N (x,y) Ψ x = M ( x, y) and Ψ y = N ( x, y) then we call the differential equation exact. In these cases we can write the differential equation as. Ψx +Ψy dy dx = 0 (3) (3) Ψ x + Ψ y d y d x = 0.
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the Test for Exactness says that the given differential equation is indeed exact (since M y = N x). This means that there exists a function f( x, y) such that and once this function f is found, the
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Some of the examples of the exact differential equations are given below: ( 2xy – 3x²) dx + ( x² – 2y ) dy equals 0 ( xy² + x ) dx + yx² dy equals 0 Cos y dx + ( y² – x sin y ) dy equals 0 ( 6x² – y
What are Exact Differential Equations? 1. A differential equation of the form M(x,y)+N(x,y)y0 =0 is called exact if and only if ∂M ∂y = ∂N ∂x. 2. If the differential equation M(x,y)+N(x,y)y0 =0 is
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