Help Me Understand Latex Derivatives: Struggling With Calculus After 2 Years

[ae4jm]

Sorry it's not the best Latex, I hope that you can still help me grasp this.

y=2xy[SUP]1[/SUP]+y(y[SUP]1[/SUP])[SUP]2[/SUP]; y[SUP]2[/SUP]=C[SUB]1[/SUB](x+1/4C[SUB]1[/SUB])

So, the solution says to implicitly differentiate and gives

y[SUP]1[/SUP]=C[SUB]1[/SUB]/2y

So, how did they get the derivative to be this? This is the first chapter in my DE class and I'm rusty with my integrals and derivatives, been about 2 years since my calc classes.

Thanks for any help...

 

[HallsofIvy]

First, it that really what they have? Is there a reason for writing "$y(y^2)^2$ rather than just $y^5$?

 

[ae4jm]

In my latex from my previous post it is actually supposed to be y prime where y is raised to the first power. But yes, this is how it was in the textbook...

Thanks for your reply...

 

[ae4jm]

Okay, I figured the derivative of

y[SUP]2[/SUP]=C[SUB]1[/SUB](X+(1/4)C[SUB]1[/SUB])

to be

 dy/dx=C[SUB]1[/SUB]/2y

But, now I can't verify the solution by plugging the derivative back into the equation, I can't get both sides equal to each other, which is what the problem is asking for. A differential equation with a solution was given; I'm supposed to find the derivative of the solution and plug it back into the differential equation to prove that the solution is actually a correct answer.

Any help? I tried plugging the derivative back into the DE and I've tried solving the solution for y and plugging that and the derivative back into the original DE but I've had no luck setting each other equal to the other. This is the same thing as solving a DE and checking your work but I can't get them to equal each other.

Thanks for any help or recommendations...

 

[ae4jm]

Please, can you guys offer me any guidance? After I find the derivative and plug it into the original DE and I solve the solution for y and plug it into the original DE I'm not getting the solution to be correct.