Find the general solution of the differential equation. (dy/dx) -2xy = (3x^2)^(x^2) ; y(0) =5?

You are correct that the solution contains an integral (I used Maple to solve the ODE), but your integral is incorrect. The correct integral is this:

∫[(3^(x^2)) * (x^2)^(x^2)] / x dx

As for evaluating the integral, I believe that this type of integral does not have a closed form solution.

I am in disbelief of how many people gave dumb answers to this question.

edit:

Here's a thought on the integration:

∫[(3^(x^2)) * (x^2)^(x^2)] / x dx

Let u = x^2

du = 2x dx

dx = du / (2x)

= ∫[(3^(u)) * (u)^(u)] / 2u dx

= (1/2) ∫[(3^(u)) * (u)^(u-1)] dx

Well, this is still not integrable.

I would leave your solution in this form:

y = ±sqrt(-∫ [(3^(x^2)) * (x^2)^(x^2)] / x dx + C)

Like whitesox said, there comes a point where you just can't get a closed form solution. The (3x^2)^(x^2) is awfully tough to integrate.

But where did all these people come from. You have no contacts.

9

i dont know that one but....

M145 Sample Quiz #1 April 01, 2004

(1a) Find

dy

dx

for y = x ln(x2 + 3).

(1b) Find

dy

dx

for y =

1

1 + e2x .

(2) Let y = f(x) = 6x − x2 + 5, for 1  x  6. For which values of x is f(x) increasing?

decreasing?

For which values of x is f(x) concave upwards? concave downwards?

What are the maximum and minimum values of f(x) (for 1  x  6). Then sketch f(x) (for

1  x  6) .

10

(3) Suppose xy2 + xy + 2 = exy. Calculate

dy

dx

at the point (x, y) = (0, 2).

(4) Let y = f(x) = x3 −

3

2

x2 − 6x + 3. Find f0(x) and f00(x).

(4a) At which points x is f0(x) = 0?

On which intervals of the x axis is f(x) increasing?

On which intervals of the x axis is f(x) decreasing?

(4b) On which intervals of the x axis is f(x) concave up?

On which intervals of the x axis is f(x) concave down?

(4c) What are the maximum and minimum values of f(x) for −3  x  3.

(4d) Sketch f(x)

−3 3

−10

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^-x)((3x^2)^(X1-45)

Physics Today, July 2005, p. 35

=

)^(x^2) ; y(0) it equals 9

Hey, I know a website that will have the answer, but I doubt your computer will let you get to it. My computer restricts it! I don't know if yours will. Maybe my mom put parental controls on my computer. I don't know why! It's a math website! OK!

its asking for x find, plug y =0 which means 0=(3x^2)^(x^2) solve for x

this is an expl.

3-4(7x8)=

(7x8) must go first

56

then

3-4=neg 4

neg 4x56=224

100,000,000,002. I don't know, really. That's just a cool number. The problem looks impossible to me. Sorry!

(dy/dx) -2 ; y(0) =5?dx) -2 ; y(0)

; y(0) =5?xy = (3x^2)^(x^2[(e^-x)

((3x^2)^(x^2= (3^2)^(x^2[(e

-2 ; y(0) =5?dx) -2 ; y(0) ; y(0) =

5?xy = (3x^2)^(x^2[) ; y(0) =5?xy

= (3x^2)^(x^2[(e^-x)((3x^2)^(x^2=

(3x^2)^(x^2[(e-2 ; y(0) =5?dx) -2

; y(0) ; y(0) =5?xy = (3x^2)^(x^2[

) ; y(0) =5?xy = (3x^2)^(x^2[(e^

-x)((3x^2)^(x^2 = (3x^2)^(x^2[(e

-2 ; y(0) =5?dx) -2; y(0) =5?xy =

(3x^2)^(x^2[(e^-x)((3x^2)^(x^2

= (3x^2)^(x^2[(e-2 ; y(0) =5?dx)

-2 ; y(0) ; y(0) =5?x