What is the solution for (dy)/(dx)+3xy^3=0,y(0)=1 ?

The solution for (dy)/(dx)+3xy^3=0,y(0)=1 is y= 1/(sqrt(3x^2+1))

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(dy)/(dx)+3xy^3=0,y(0)=1

\frac{d y}{d x} + 3 x y^{3} = 0, y (0) = 1

y = \frac{1}{3 x ^{2} + 1}

Solution steps

\frac{d y}{d x} + 3 x y^{3} = 0

Solve separable ODE:

y = \frac{1}{3 x ^{2} + 1}

y = \frac{1}{3 x ^{2} + 1}

\int \frac{5 e ^{2 x} - e ^{x}}{e ^{2 x} - 1} d x

\frac{\partial}{\partial x} (9 x^{2} y^{2})

\int (x^{2} e^{2 x} - 3 x e^{2 x} + 5 e^{2 x}) d x

\int_{2}^{6} 8 d x

x \to 0 lim (3 sin (x) - 1)

What is the solution for (dy)/(dx)+3xy^3=0,y(0)=1 ?
The solution for (dy)/(dx)+3xy^3=0,y(0)=1 is y= 1/(sqrt(3x^2+1))