- #1
SmashtheVan
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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.