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

sorry der’s a little mistake
dy/dx + y(1-x)x½ =1-x1/2

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

It is a 1st 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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