need help solving (1)/(x) (dy)/(dx) = y e^(x^2) + 2 squareroot(y) e^(x^2)

[abel muroi]

I was given this equation

(1)/(x) (dy)/(dx) = y e^x2 + 2 squareroot(y) e^x2

and was told to solve it..

I know that i have to collect all the y terms on one side and all the x terms on the other, and then im supposed to take the integral of both sides and simplify as much as possible.

But i am having a bit of trouble on collecting the terms. Should i subtract (1)/(x) from both sides and divide y from both sides?

 

[Ishuda]

I was given this equation

(1)/(x) (dy)/(dx) = y e^x2 + 2 squareroot(y) e^x2

and was told to solve it..

I know that i have to collect all the y terms on one side and all the x terms on the other, and then im supposed to take the integral of both sides and simplify as much as possible.

But i am having a bit of trouble on collecting the terms. Should i subtract (1)/(x) from both sides and divide y from both sides?

I believe your equation is
\(\displaystyle \dfrac{1}{x}\,\, \dfrac{dy}{dx}\, =\, y\, e^{x^2}\, +\, 2\, \sqrt{y}\, e^{x^2}\)

If so, try factoring the right hand side then multiplying by x.

 

[abel muroi]

I believe your equation is
\(\displaystyle \dfrac{1}{x}\,\, \dfrac{dy}{dx}\, =\, y\, e^{x^2}\, +\, 2\, \sqrt{y}\, e^{x^2}\)

If so, try factoring the right hand side then multiplying by x.

Ok so i factored the right hand side and got this..

(1)/(x) = e^(x²)(y + 2squareroot(y))

then i multiplied both side by x to remove the fraction on the left side.

1 = x e^(x² )(y + 2squareroot(y))

should i take the integral of both sides? or can i simplify this more?

 

[pythagorean314159]

separable equations

I was given this equation

(1)/(x) (dy)/(dx) = y e^x2 + 2 squareroot(y) e^x2

and was told to solve it..

I know that i have to collect all the y terms on one side and all the x terms on the other, and then im supposed to take the integral of both sides and simplify as much as possible.

But i am having a bit of trouble on collecting the terms. Should i subtract (1)/(x) from both sides and divide y from both sides?

This is an example of separable differential equations.

First, factor out e^{x^2} from the right side of the equation. Then, multiply by x dx on both sides. Afterwards, divide by y + 2 sq.rt. y on both sides...You should have something like this...

1
--------------- dy = xe^{x^2}dx
y + 2 sq.rt y

Now, you can continue to solve the differential equation.

 

[Ishuda]

Ok so i factored the right hand side and got this..

(1)/(x) = e^(x²)(y + 2squareroot(y))

then i multiplied both side by x to remove the fraction on the left side.

1*dy/dx = x e^(x² )(y + 2squareroot(y))

should i take the integral of both sides? or can i simplify this more?

You dropped the dy/dx. What you should have got was
\(\displaystyle \dfrac{dy}{dx}\, =\, x\, e^{x^2}\, [y\, +\, 2\, \sqrt{y}]\)
How would you get all of the x's on one side and all of the y's on the other?