- #1

SmashtheVan

- 42

- 0

## Homework Statement

Solve the equation:

[tex](x+xy^{2})dx + e^{x^{2}}y dy =0[/tex]

## Homework Equations

n/a

## The Attempt at a Solution

i) [tex]xdx(1+y^{2}) = -e^{x^{2}}y dy[/tex]

(multiply both sides by 2 to prepare for integration:

ii) [tex]\frac{-2xdx}{e^{x^{2}}}= \frac{2y dy}{1+y^{2}}[/tex]

integrate and get:

iii) [tex]\frac{1}{e^{x^{2}}}= ln(1+y^{2}) + C[/tex]

first integral was acheived from Maple, I am not sure if its what should be used here, but its what i have for now

iv) exponentiate both sides to remove natural log:

[tex]e^{e^{-x^{2}}}=1 + y^{2} + C[/tex]

v)combine constants, separate y

[tex] y^{2} = e^{e^{-x^{2}}} - C [/tex]

vi)square root of the system:

[tex]y=\sqrt{ e^{e^{-x^{2}}}} -C[/tex]Does this seem like a reasonable answer? I'm wary because of the occurance of the exponential function, raised to the exponential function.