What is the solution for (dy)/(dx)=14y+1,y=-1/14+12e^{14x} ?

The solution for (dy)/(dx)=14y+1,y=-1/14+12e^{14x} is y=(e^{14x+c_{1}})/(14)-1/14

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(dy)/(dx)=14y+1,y=-1/14+12e^{14x}

\frac{d y}{d x} = 14 y + 1, y = - \frac{1}{14} + 12 e^{14 x}

y = \frac{e ^{14 x + c_{1}}}{14} - \frac{1}{14}

Solution steps

\frac{d y}{d x} = 14 y + 1

Solve separable ODE:

y = \frac{e ^{14 x + c_{1}}}{14} - \frac{1}{14}

y = \frac{e ^{14 x + c_{1}}}{14} - \frac{1}{14}

(9 x^{2} + 2 x) d x + (12 y^{3} - 4 y) d y = 0

\frac{d y}{d x} = 2 x^{5} y

\frac{d N}{d t} + N = N \cdot t e^{t + 2}

\frac{d y}{d x} = \frac{( y x + 5 x )}{x ^{2} + 1}

y^{^{'}} - 3 y sin (3 t) = - 3 sin (3 t), y (\frac{π}{6}) = 2

What is the solution for (dy)/(dx)=14y+1,y=-1/14+12e^{14x} ?
The solution for (dy)/(dx)=14y+1,y=-1/14+12e^{14x} is y=(e^{14x+c_{1}})/(14)-1/14