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Consider the differential equation dydx=6x, dydx=6x, with initial condition y(0)=4y(0)=4.
a. use euler's method with two steps to estimate yy when x=1x=1: y(1)≈y(1)≈ equation editorequation editor

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cdw2014
Formatting is kind of messed up. I'm assuming the differential equations is dy/dx = 6x

You need to get all the x's on one side and y'all on the other.

dy =6x dx

Integrate both sides.

y = 3x^2 + C

Now plug in the given values

y(0) = 4 = 3(0)^2 + C

C = 0

y = 3x^2

Plug 1 in for x to find the value of y(1)

y(1) = 3(1)^2 = 3

In the differential equation, we have separated the variable and then integrate the equation. Then the equation is y = 3x² + 4.

What is integration?

It is the reverse of differentiation.

The differential equation is given as

[tex]\rm \dfrac{dy}{dx}=6x[/tex]

With initial condition y(0) = 4.

Separate the variables

[tex]\rm dy = 6x\ dx[/tex]

On integrating both sides, we have

[tex]\rm \int dy = \int 6x\ dx\\\\y \ \ = 3x^{2} + c[/tex]

At x = 0, the value of y is 4. Then

[tex]\rm y = 3x^{2} + c\\\\ c=y - 3x^{2} \\\\c = 4 - 3 (0)^2\\\\c = 4[/tex]

The equation is y = 3x² + 4.

More about the integration link is given below.

https://brainly.com/question/18651211

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