In each of the Exercises 1 to 10, show t...

In each of the Exercises 1 to 10, show that the given differential equation is homogeneous and solve each of them.
`(x^(2) + xy) dy = (x^(2) + y^(2))dx`.

Text Solution

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The correct Answer is:

`(x - y)^(2) = Cx e^(-y)/(x)`

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NCERT GUJARATI-DIFFERENTIAL EQUATIONS-EXERCISE - 9.5

In each of the Exercises 1 to 10, show that the given differential equ...
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y ' = (x+ y)/(x)
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(x - y)dy - (x + y) dx = 0
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(x^(2) - y^(2)) dx + 2xy dy = 0
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x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy
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x dy - y dx = sqrt(x^(2) + y^(2)) dx
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{ xcos ((y)/(x)) + y sin ((y)/(x))} y dx = { y sin ((y)/(x)) - x cos (...
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(1 + e^(x)/(y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0
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For each of the differential equations in Exercises from 11 to 15, fin...
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