(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the equation:

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

2. Relevant equations

n/a

3. 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, im 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.

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# Diff EQ- exponential raised to the exponential?

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