# particular solution of the given differential equation

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?

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 $C$ $$-\frac{1}{e^{12}}=\frac{3}{e}+C$$
• $-\frac{1}{e^{-12}}$ or $-\frac{1}{e^{12}}$? – Motun Jun 21 '16 at 8:06