Question
Asked Jul 22, 2019
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Solve the first order differential equation using any acceptable method.

(6x+1)y2 dy/dx+3x2+2y3=0,    y(0)=1

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Expert Answer

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Step 1

Given the differential equation is

Now separate the variables as follows

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dy (6x+1) y2 3x +2y = 0 dx (6x+1)y'dy+(3x2 +2y?)dk 0 (6ay2 +1y)dy +(3x2 +2y' )ck= 0

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Step 2

Then,

 

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Comparing with mdx + ndy = 0 n(6xy2 +1y2 m(3x2 +2y

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Step 3

Then take partial differentiation,

Hence th...

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= 6y an = 6y2

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