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Solve the following differential equation (x2 − yx2 ) dy + (y2 + xy2) dx = 0 - Mathematics and Statistics

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Sum

Solve the following differential equation

(x2 − yx2 ) dy + (y2 + xy2) dx = 0

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Solution

(x2 − yx2 ) dy + (y2 + xy2) dx = 0

∴ x2 (1 - y) dy = - y2 (1 + x) dx

∴ `((1-y)/y^2)dy = - ((1+x)/x^2)dx`

Integrating on both sides, we get

`int(1/y^2- 1/y) dy = - int (1/x^2+1/x)dx`

∴ `-1/y - log |y| = - (-1/x + log  | x |)+c`

∴`(-1)/y - log |y| = 1/x - log  | x |+c`

∴ `log  | x | - log | y | = 1/x + 1/y + c`

Concept: Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.3 | Q 1.3 | Page 165
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