Question

y' + y*x^2 = 0
y(0) = -2

Answer 1

\[\frac{dy}{dx} + y*x^2 = 0 \]
\[ \frac{dy}{dx} = -y*x^2\]
\[ \frac{1}{y}dy = -x^2dx\]
\[\log_e y + C_1 =-\frac{x^3}{3} + C_2\]
\[ \log_ey +\frac{x^3}{3} + C = 0 \]
\[C = C_1 - C_2\]

Answer 2

y(x) = c_1 e^(-x^3/3)