Final Answer
$y=\frac{\tan\left(2\left(\frac{1}{4}\ln\left(-\sqrt{2}x+1\right)+\frac{1}{4}\ln\left(\sqrt{2}x+1\right)+C_0\right)\right)}{2}$
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Step-by-step Solution
Problem to solve:
$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$
Specify the solving method
1
Grouping the terms of the differential equation
$\left(1+x^4\right)dy=-x\left(1+4y^2\right)dx$
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 of the equality. 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.
Final Answer
$y=\frac{\tan\left(2\left(\frac{1}{4}\ln\left(-\sqrt{2}x+1\right)+\frac{1}{4}\ln\left(\sqrt{2}x+1\right)+C_0\right)\right)}{2}$