What is the solution for (dy)/(dx)=c_{1}y+1 ?

The solution for (dy)/(dx)=c_{1}y+1 is y=(e^{xc_{1}+c_{1}})/(c_{1)}-1/(c_{1)}

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(dy)/(dx)=c_{1}y+1

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d v}{d t} = g - k v (t), v = 0, t = 0

\frac{d y}{d x} + 2 y = 11

\frac{d y}{d x} y = e^{x^{2 l n (x)}}

x^{^{'}} = (x)^{45 + 2} (ln (t) + (2 + 2) t e^{t})

y^{^{'}} = x^{3} y

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