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- Equation différentielle exacte
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- Produit de binômes avec terme commun
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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
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$\frac{1}{y^2-1}dy=\left(1+e^{-x}\right)dx$
Learn how to solve problems step by step online. dy/dx=(1+e^(-x))(y^2-1). 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. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=1+e^{-x}, b=\frac{1}{y^2-1}, dyb=dxa=\frac{1}{y^2-1}dy=\left(1+e^{-x}\right)dx, dyb=\frac{1}{y^2-1}dy and dxa=\left(1+e^{-x}\right)dx. Expand the integral \int\left(1+e^{-x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the integral \int\frac{1}{y^2-1}dy and replace the result in the differential equation.
