Solve-dy-dx-1-2-y-3-2-with-y-0-4-

Question Number 17322 by tawa tawa last updated on 04/Jul/17

Solve : \frac{dy}{dx} + \frac{1}{2} y = \frac{3}{2} with y (0) = 4

Answered by mrW1 last updated on 04/Jul/17

2 \frac{dy}{dx} = 3 - y

- \frac{dy}{y - 3} = \frac{dx}{2}

\int \frac{dy}{y - 3} = - \int \frac{dx}{2}

\ln ∣ y - 3 ∣= - \frac{x}{2} + C

y (0) = 4

\ln (1) = 0 + C

\Rightarrow C = 0

\ln ∣ y - 3 ∣= - \frac{x}{2}

y - 3 = \pm e^{- \frac{x}{2}}

y = 3 \pm e^{- \frac{x}{2}}

since y (0) = 4

\Rightarrow y = 3 + e^{- \frac{x}{2}}

Commented by tawa tawa last updated on 04/Jul/17

God bless you sir .

Commented by tawa tawa last updated on 04/Jul/17

How is C = 0 sir ? ? ?

Commented by mrW1 last updated on 04/Jul/17

i changed my answer . there are 2

possible solutions .

Commented by tawa tawa last updated on 04/Jul/17

God bless you sir .