# 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. Integrate both sides, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{1+4y^2}dy and replace the result in the differential equation.

$\tan\left(\arctan\left(2y\right)\right)=\tan\left(2\left(-\frac{1}{2}\arctan\left(\sqrt{2}\left(x-\frac{\sqrt{2}}{2}\right)\right)+\frac{1}{2}\arctan\left(\sqrt{2}\left(x+\frac{\sqrt{2}}{2}\right)\right)+C_0\right)\right)$

### Problem Analysis

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

### Main topic:

Differential equations

~ 0.73 seconds