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Popular >

(1+4x^2)y^'=1

Solution

(1 + 4 x^{2}) y^{^{'}} = 1

Solution

y = \frac{1}{2} arctan (2 x) + c_{1}

Solution steps

(1 + 4 x^{2}) y^{'} (x) = 1

Isolate

y^{'} (x) : y^{'} (x) = \frac{1}{1 + 4 x ^{2}}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{1}{1 + 4 x ^{2}} d x

\int \frac{1}{1 + 4 x ^{2}} d x = \frac{1}{2} arctan (2 x) + c_{1}

y = \frac{1}{2} arctan (2 x) + c_{1}

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Frequently Asked Questions (FAQ)

What is the solution for (1+4x^2)y^'=1 ?
The solution for (1+4x^2)y^'=1 is y= 1/2 arctan(2x)+c_{1}