Solve the Initial Value problem

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Homework Help Overview

The discussion revolves around solving an initial value problem involving a differential equation of the form dy/dt = t^2 * y^3, with the initial condition y(0) = -1.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the problem by separating variables and integrating both sides. Some participants question the correctness of the setup and the handling of the integration process. There is also a query regarding the application of the initial condition after integration.

Discussion Status

Participants are actively engaging with the problem, providing guidance on the integration process and the subsequent use of the initial condition. Multiple interpretations of the steps involved are being explored, particularly concerning the integration and the determination of the constant.

Contextual Notes

There is a noted confusion regarding the initial condition y(0) = -1 and how it fits into the solution after integration. The discussion reflects on the necessity of correctly applying this condition to find the constant of integration.

lmanri
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dy/dt=t^(2)y^(3) , y(0)=-1

I need help solving this

I put the integral (dy/y^3)= integral (t^2)dt
but idk what to do after that or if that's even right
 
Last edited:
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Hi Imanri,

You dropped an integral sign...

[tex]\int{\frac{dy}{y^3}}=\int{t^2dt}[/tex]

Do the integration on both sides.

ehild
 
Thank you, but after I find that what do I do with y(0)=1
 
You have an undetermined constant after integration. Substitute t=0 and y=-1 in your integral and solve for c.

ehild
 
Thank you
 
What is your solution?

ehild
 
y=-1/(t^(3)+C)
 

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