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Differential Equation Help A2 maths Help

The variables 𝑥 and 𝑦 are related by a differential equation

However, Im at a bit of a loss as to where to go once I have found the equation, as I know I have to work out C. Do i do this by putting e to the power of each side of the equation, as the y and x values both have ln (and would I have to also put eC) or should I rearrange this equation for C and substitute in the values for x and y???
(edited 4 years ago)
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mqb2766
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Original post by mushed
The variables 𝑥 and 𝑦 are related by the differential equation
d𝑦/d𝑥= (6𝑦𝑒3𝑥)/(2 + 𝑒3𝑥)
Given that 𝑦 = 36 when 𝑥 = 0, find an expression for 𝑦 in terms of x

So far, I have found that lny= ln(2+e3x)2 +C

However, Im at a bit of a loss as to where to go from here, I know I have to work out C. Do i do this by putting e to the power of each side of the equation (and would I have to also put eC) or should I rearrange this equation for C and substitute in the values for x and y???

I'm losing some of your formatting but writing the constant as + ln(C) means you can combine and take inverse logs.
Then get C by subbing in the initial values.
(edited 4 years ago)

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