Question

solve the differential equation: dy/dx=y+2
find the particular solution of this equation that satisfies the initial condition y(0)=15

Answer 1

my trying :
we have to separate the variables
\[dy \div y+2=dx\]
\[dy \div y + dy \div 2=dx\]

however this is my trying to separate the variables, might be wrong :(

now I have to problem, how to separate the variables in this eqation
the second problem, how to integrate dx,?
you know because we have to integrate both sides after separating the variables

thanx :)

Answer 2

actually I even don't know how integrate the left side also because there are dy twice, that if my separating is true

Answer 3

\[\frac{dy}{dx}=y+2\\
\frac{dy}{y+2}=dx\\
\ln(y+2)=x+C\\
y+2=e^{x+C}\\
y=Ae^x-2\ \text{where }A=e^C\\
15=A-2 \Rightarrow A=17\\
y=17e^x-2\]

Answer 4

that awesome work, thank you so much :)

Answer 5

I'm working to understand all the steps :)