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Popular Calculus >

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

Solution

y^{^{'}} = \frac{x}{1 + x ^{2}}

Solution

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

Solution steps

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

If

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

then

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

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

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

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

Graph

Popular Examples

derivative of ((x+1^3)/x)

\frac{d}{d x} (\frac{( x + 1 ) ^{3}}{x})

y^{^{'}} = y^{2} - (x y)^{2}

integral of 1/(3sqrt(x)(2+\sqrt{x))}

\int \frac{1}{3 x ( 2 + x )} d x

limit as x approaches 2-of arcsin(x/2)

x \to 2 - lim (arcsin (\frac{x}{2}))

limit as x approaches-1 of (x+2x^4)^3

x \to - 1 lim ((x + 2 x^{4})^{3})

Frequently Asked Questions (FAQ)

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