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Popular >

(dy)/(dx)=-1/3 x^3

Solution

\frac{d y}{d x} = - \frac{1}{3} x^{3}

Solution

y = - \frac{x ^{4}}{12} + c_{1}

Solution steps

\frac{d y}{d x} = - \frac{1}{3} x^{3}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = - \frac{1}{3} x^{3}

If

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

then

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

y = \int - \frac{1}{3} x^{3} d x

\int - \frac{1}{3} x^{3} d x = - \frac{x ^{4}}{12} + c_{1}

y = - \frac{x ^{4}}{12} + c_{1}

Popular Examples

(d^2)/(dx^2)(x+1/x)

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

integral of (cos(2x))/(cos(x))

\int \frac{cos ( 2 x )}{cos ( x )} d x

8x^2y^'=y^'+8xe^{-y}

8 x^{2} y^{^{'}} = y^{^{'}} + 8 x e^{- y}

derivative of f(x)=-7sqrt(x)-2/(x^7)derivative of

f (x) = - 7 x - \frac{2}{x ^{7}}

(\partial)/(\partial x)(arctan(y))

\frac{\partial}{\partial x} (arctan (y))

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=-1/3 x^3 ?
The solution for (dy)/(dx)=-1/3 x^3 is y=-(x^4)/(12)+c_{1}