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Differential Calculus> sorry der’s a little mistake dy/dx + y(1-...

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sorry der’s a little mistake
dy/dx + y(1-x)x^½=1-x^1/2

vishakha , 11 Years ago

Grade 11

1 Answers

Jitender Singh

Last Activity: 11 Years ago

Ans:
Hello Student,
Please find answer to your question below

It is a 1^st orderlinear differential equation.
$\frac{dy}{dx} + Py = Q$
Integrated Factor (IF):
$IF = e^{\int Pdx}$
$\frac{dy}{dx} + \sqrt{x}(1-x)y = 1-\sqrt{x}$
$P = \sqrt{x}(1-x)$
$IF = e^{\int \sqrt{x}(1-x)dx}$
$IF = e^{\int (\sqrt{x}-x^{3/2})dx}$
$IF = e^{(\frac{2}{3}x^{3/2}-\frac{2}{5}x^{5/2})}$

Solution of the equation:
$y(IF) = \int (IF)Qdx$

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