Step-by-step Solution

Solve the differential equation $\left(1+x^4\right)dy+x\left(1+4y^2\right)dx=0$

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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.

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

Unlock this full step-by-step solution!

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 of the differential equation, the left side with respect to y, and the right side with respect to x. Taking the constant (-1) out of the integral.

Final Answer

$y=\frac{\tan\left(2\left(-\frac{1}{2}\arctan\left(x^{2}\right)+C_0\right)\right)}{2}$
$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

Time to solve it:

~ 1.86 s (SnapXam)