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 )}

\int \frac{( 2 r + 1 )}{r ^{2} - 3 r + 2} d r

x \to 10 lim (\frac{1}{( x - 10 ) ^{2}})

\frac{e ^{- 4 s}}{s ^{3}}

\int x 25 - x^{2} d x

\int tan^{3} (d) x d x

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)}