What is the solution for (dy)/(dx)y=x^{4x} ?

The solution for (dy)/(dx)y=x^{4x} is y=sqrt(2*integral of x^{4x)},y=-sqrt(2*integral of x^{4x)}

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(dy)/(dx)y=x^{4x}

\frac{d y}{d x} y = x^{4 x}

y = 2 \cdot \int x^{4 x} d x, y = - 2 \cdot \int x^{4 x} d x

Solution steps

\frac{d y}{d x} y = x^{4 x}

Solve separable ODE:

y = 2 \cdot \int x^{4 x} d x, y = - 2 \cdot \int x^{4 x} d x

y = 2 \cdot \int x^{4 x} d x, y = - 2 \cdot \int x^{4 x} d x

\frac{d y}{d x} y = cosh^{2} (3 x) - sinh (x^{2})

\frac{d y}{d x} = \frac{3 + 12 x}{x y ^{2}}, x > 0

y^{^{'}} - \frac{( t + 1 ) y}{t ^{2}} = \frac{1}{t} + \frac{1}{t ^{2}}

y^{^{'}} = - (- \frac{x ^{2}}{3 y})

\frac{d y}{d x} = 2 x^{3} y

What is the solution for (dy)/(dx)y=x^{4x} ?
The solution for (dy)/(dx)y=x^{4x} is y=sqrt(2*integral of x^{4x)},y=-sqrt(2*integral of x^{4x)}