Initial Condition Statement: evaluate dy/dx = x^2/y^2 with y(0) = 2

[BigNate]

Hello Everyone,

I'm hoping someone can help point me in the right direction. I'm trying to evaluate dy/dx = x^2/y^2 with initial condition statement y(0)=2

Here's how I think I would solve this...
Put all the y's on left side, all the x's on right side:
y^2dy=x^2dx
Integrate:
y^3+C=x^3+C
Simplify
y=x+C

Now taking the initial condition given in question y(0) = 2, this tells me C is 2
Answer: y=x + 2

Can someone please tell me if this is correct?

 

[Deleted member 4993]

Hello Everyone,

I'm hoping someone can help point me in the right direction. I'm trying to evaluate dy/dx = x^2/y^2 with initial condition statement y(0)=2

Here's how I think I would solve this...
Put all the y's on left side, all the x's on right side:
y^2dy=x^2dx
Integrate:
y^3+C=x^3+C ← Don't constant of integration on both sides
Simplify
y=x+C → No.... That "simplification" is not correct

Now taking the initial condition given in question y(0) = 2, this tells me C is 2
Answer: y=x + 2

Can someone please tell me if this is correct?

y^3 = x^3 + C &

y(0) = 2 →

C = 8 ... and finish it....

 

[BigNate]

Oh, so I should have taken x^(1/3) as well as C^(1/3)? Which makes C=8.

So would the answer then be y= (x+8)^(1/3)?

Thanks for your help and time!

 

[Deleted member 4993]

Oh, so I should have taken x^(1/3) as well as C^(1/3)? Which makes C=8.

So would the answer then be y= (x+8)^(1/3)? ................... Incorrect

Thanks for your help and time!

y = (x^3 + 8)^(1/3)