What is the solution for (dy)/(dx)=e^{-a*x}-b*y,y(0)=0 ?

The solution for (dy)/(dx)=e^{-a*x}-b*y,y(0)=0 is y= 1/(e^{ax)(-a+b)}-1/(e^{bx)(b-a)}

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(dy)/(dx)=e^{-ax}-by,y(0)=0

\frac{d y}{d x} = e^{- a \cdot x} - b \cdot y, y (0) = 0

y = \frac{1}{e ^{a x} ( - a + b )} - \frac{1}{e ^{b x} ( b - a )}

Solution steps

\frac{d y}{d x} = e^{- a \cdot x} - b \cdot y

Solve linear ODE:

y = \frac{1}{e ^{a x} ( - a + b )} - \frac{1}{e ^{b x} ( b - a )}

y = \frac{1}{e ^{a x} ( - a + b )} - \frac{1}{e ^{b x} ( b - a )}

What is the solution for (dy)/(dx)=e^{-a*x}-b*y,y(0)=0 ?
The solution for (dy)/(dx)=e^{-a*x}-b*y,y(0)=0 is y= 1/(e^{ax)(-a+b)}-1/(e^{bx)(b-a)}