# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

Learn how to solve differential equations problems step by step online.

$\left(1+x^4\right)dy=-x\left(1+4y^2\right)dx$

Learn how to solve differential equations problems step by step online. Solve the differential equation (1+x^4)dy+x(1+4y^2)*dx=0. Grouping the terms of the differential equation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side. Simplify the expression \frac{-x}{1+x^4}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

$y=\frac{\tan\left(2\left(-\frac{3}{5}\arctan\left(\frac{6}{\sqrt{18}}x-1\right)+\frac{7}{101}+\frac{1}{5}\ln\left(\sqrt{1+x^2-\frac{6}{\sqrt{18}}x}\right)-\frac{1}{5}\ln\left(x+\frac{6}{\sqrt{18}}\right)+C_0\right)\right)}{2}$
$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$