Question

who can find this..? y'=y ,,,find the general equetion,,,please help

Answer 1

\[\frac{dy}{dx}=y\]This is a separable ordinary differential equation, so\[\frac{dy}{y}=dx\]You now integrate both sides,\[\int\limits_{}^{}\frac{dy}{y}=\int\limits_{}{}dx \rightarrow \ln(y)=x+c\]Exponentiate both sides to solve for y (which is what you need),\[e^{\ln(y)}=e^{x+c}\]The left-hand side is just\[e^{\ln(y)}=y\]by definition of natural logarithm, while the right-hand side is just,\[e^{x+c}=e^ce^x=Ae^x\]because e^c is just a constant.Therefore\[y=Ae^x\]