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Popular >

(dy)/(dx)=x^2+1

Solution

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

Solution

y = \frac{x ^{3}}{3} + x + c_{1}

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

If

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

then

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

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

\int x^{2} + 1 d x = \frac{x ^{3}}{3} + x + c_{1}

y = \frac{x ^{3}}{3} + x + c_{1}

Popular Examples

derivative of 8sqrt(7x^2+5)

\frac{d}{d x} (8 7 x^{2} + 5)

integral of (e^x)/(sqrt(4+e^{2x))}

\int \frac{e ^{x}}{4 + e ^{2 x}} d x

derivative of x/(x-10)

\frac{d}{d x} (\frac{x}{x - 10})

(dy)/(dx)=(2x-3)/(5y)

\frac{d y}{d x} = \frac{2 x - 3}{5 y}

derivative of ((x^3-x)/(1+x^2))

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

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=x^2+1 ?
The solution for (dy)/(dx)=x^2+1 is y=(x^3)/3+x+c_{1}