Final answer to the problem
$y=C_1e^{8x}$
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Step-by-step Solution
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- Equation différentielle exacte
- Équation différentielle linéaire
- Équation différentielle séparable
- Equation différentielle homogène
- Produit de binômes avec terme commun
- Méthode FOIL
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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
$\frac{1}{8y}dy=dx$
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$\frac{1}{8y}dy=dx$
Learn how to solve problems step by step online. dy/dx=8y. 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=dx\to \int bdy=\int1dx, where b=\frac{1}{8y}. Solve the integral \int\frac{1}{8y}dy and replace the result in the differential equation. Solve the integral \int1dx and replace the result in the differential equation.
Final answer to the problem
$y=C_1e^{8x}$
