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Exercise

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

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation e^x(y^2-4y)dx+4dy=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{4}{y^2-4y}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation e^x(y^2-4y)dx+4dy=0

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Final answer to the exercise

$-\ln\left|y\right|+\ln\left|y-4\right|=-e^x+C_0$

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$-40+15+10-80$
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