What is the solution for (dy)/(dx)=14e^{5x-y},y(0)=0 ?

The solution for (dy)/(dx)=14e^{5x-y},y(0)=0 is y=ln(14/5 e^{5x}-9/5)

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(dy)/(dx)=14e^{5x-y},y(0)=0

\frac{d y}{d x} = 14 e^{5 x - y}, y (0) = 0

y = ln (\frac{14}{5} e^{5 x} - \frac{9}{5})

Solution steps

\frac{d y}{d x} = 14 e^{5 x - y}

Solve separable ODE:

y = ln (\frac{14}{5} e^{5 x} - \frac{9}{5})

y = ln (\frac{14}{5} e^{5 x} - \frac{9}{5})

\frac{d y}{d t} = \frac{( 3 t ^{2} + 4 t + 2 )}{2 ( y - 1 )}

(x^{2} + y^{2}) (x d y + y d x) - x y (x d x + y d y) = 0

y^{^{'}} - x (y - 1) = 0

y^{^{'}} = x + x y + 1 + y

\frac{d y}{d x} = \frac{9 + 17 x}{x y ^{2}}, x > 0, y (1) = 2

What is the solution for (dy)/(dx)=14e^{5x-y},y(0)=0 ?
The solution for (dy)/(dx)=14e^{5x-y},y(0)=0 is y=ln(14/5 e^{5x}-9/5)