What is the solution for y^'=-a*y+b*y ?

The solution for y^'=-a*y+b*y is y=(e^{-at+bt-c_{1}a+c_{1}b})/(a-b)

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y^'=-ay+by

y^{^{'}} = - a \cdot y + b \cdot y

y = \frac{e ^{- a t + b t - c_{1} a + c_{1} b}}{a - b}

Solution steps

y^{'} (t) = - a \cdot y + b \cdot y

Solve separable ODE:

y = \frac{e ^{- a t + b t - c_{1} a + c_{1} b}}{a - b}

y = \frac{e ^{- a t + b t - c_{1} a + c_{1} b}}{a - b}

What is the solution for y^'=-a*y+b*y ?
The solution for y^'=-a*y+b*y is y=(e^{-at+bt-c_{1}a+c_{1}b})/(a-b)