# First order ODE initial value problem

1. Homework Statement

Given the below stated equations I need to find the exact polynomial given the initial condition.

y(0) = 1
y = 4*t*sqrt(y)

2. Homework Equations

3. The Attempt at a Solution

I simply disregard the initial value condition and get y = t^4

How can I find the fourth order polynomial with the given initial value?

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Is it not possible to integrate a first order differential equation and also consider the initial value y(0) = 1 ?

Isn't there a typo? Where is y' ?

I assume the equation is written y'=4ty^(1/2) in which case it appears you have dy/dt=y' and this is a seperable equation. Solve for y and then solve for the initial value.

HallsofIvy
Homework Helper
1. Homework Statement

Given the below stated equations I need to find the exact polynomial given the initial condition.

y(0) = 1
y = 4*t*sqrt(y)

2. Homework Equations

3. The Attempt at a Solution

I simply disregard the initial value condition and get y = t^4

How can I find the fourth order polynomial with the given initial value?

The differential equation is $\frac{dy}{dt}= 4t\sqrt{y}= 4ty^{\frac{1}{2}}$
That can be written $y^{-\frac{1}{2}}dy= 4t dt$. Now integrate both sides.