Find the general solution to dy/dx = 2y passing through the point (5, 1)

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AamiaO196114 AamiaO196114

03-11-2022
Mathematics

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Find the general solution to dy/dx = 2y passing through the point (5, 1)

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LionelR658921 LionelR658921 · Answer 1 · 2022-11-03T15:28:23-04:00

LionelR658921 LionelR658921

03-11-2022

We will have the following:

[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]

Then we find "c":

[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]

Thus, the general solution passing through (5, 1) is:

[tex]\frac{\log(y)}{2}=x-5[/tex]

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