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I need help with this calculus problem I am very confused about how to go through with this problem!

Find the particular solution of the given differential equation $$\frac{\text{d}y}{\text{d}x}=−6xe^{y−x^2}$$with $y=12$ when $x=1$.

Can anyone help walk me through this?

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Use separation of variables, note that$$\frac{\text{d}y}{\text{d}x}=−6xe^{y}e^{−x^2}$$or$$e^{-y} \ \text{d}y =−6xe^{−x^2} \ \text{d}x$$Integrate both sides, you will get$$-e^{-y}=3e^{-x^2}+C$$And using the condition $y(1)=12$, find the value of constant $C$ $$-\frac{1}{e^{12}}=\frac{3}{e}+C$$

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  • $\begingroup$ what answer did you get? or could you show me your steps? $\endgroup$ – google Jun 21 '16 at 7:59
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    $\begingroup$ Which part is not clear in my solution? $\endgroup$ – Ghartal Jun 21 '16 at 8:02
  • $\begingroup$ $-\frac{1}{e^{-12}}$ or $-\frac{1}{e^{12}}$? $\endgroup$ – Motun Jun 21 '16 at 8:06

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