solve the separable differential equation and find the particular solution satisfying the initial condition

Question

Solve the separable differential equation dy/dx=0.9y,

and find the particular solution satisfying the initial condition y(0)=−6.

y(x)=

Answer 1

Divide the y to the dy side but leave the coefficient for the dx. Integrate both sides and include an unknown constant (+c, there's actually two of them, but you can combine them to one on the right).

ln|y| = 0.45x^2 + C

You raise both sides as powers of e to get rid of the natural log. and then change e^C to a coefficient K.

y=Ke^.45x^2

Solve for K by plugging in the given point.