What is the solution for x^'=6c_{1}-(3x)/5 ?

The solution for x^'=6c_{1}-(3x)/5 is x=-(e^{(-3t-c_{1})/5})/(3)+10c_{1}

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x^'=6c_{1}-(3x)/5

x^{^{'}} = 6 c_{1} - \frac{3 x}{5}

x = - \frac{e ^{\frac{- 3 t - c _{1}}{5}}}{3} + 10 c_{1}

Solution steps

x^{'} (t) = 6 c_{1} - \frac{3 x}{5}

Solve separable ODE:

x = - \frac{e ^{\frac{- 3 t - c _{1}}{5}}}{3} + 10 c_{1}

x = - \frac{e ^{\frac{- 3 t - c _{1}}{5}}}{3} + 10 c_{1}

\int_{0}^{1} x (1 - x^{2}) d x

f (t) = \frac{t ^{2}}{2}

\frac{d}{d x} (\frac{x ^{4} + 1}{x ^{2}})

\frac{d}{d x} (5 e^{- 4 x})

f^{^{'}} (x) = x^{(2)} - 4

What is the solution for x^'=6c_{1}-(3x)/5 ?
The solution for x^'=6c_{1}-(3x)/5 is x=-(e^{(-3t-c_{1})/5})/(3)+10c_{1}