(x+y)dydx=1 #10; #10; =0 (x+y)dy=dx #10; #10; =0 dxdy+( 1)x=y #10; #10;I.F =e^∫ 1dy=e^ y #10; #10; ∴ Required soln; ...

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Linear Differential Equations of First Order

Solve: x+yd...

Question

Solve:
$(x + y) \frac{d y}{d x} = 1$

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Solution

$(x + y) \frac{d y}{d x} = 1$

$= 0 (x + y) d y = d x$

$= 0 \frac{d x}{d y} + (- 1) x = y$

I.F $= e^{\int - 1 d y} = e^{- y}$

$∴$ Required soln;

$x \times$ I.F $= \int y \times e^{- y} d y + + c$

By integration, we get $x + y + 1 = c e^{y}$

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