What is the solution for (dy)/(dx)=(2y+5)/(-5x-2) ?

The solution for (dy)/(dx)=(2y+5)/(-5x-2) is y=(c_{1})/(2(-5x-2)^{2/5)}-5/2

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(dy)/(dx)=(2y+5)/(-5x-2)

\frac{d y}{d x} = \frac{2 y + 5}{- 5 x - 2}

y = \frac{c _{1}}{2 ( - 5 x - 2 ) ^{\frac{2}{5}}} - \frac{5}{2}

Solution steps

\frac{d y}{d x} = \frac{2 y + 5}{- 5 x - 2}

Solve separable ODE:

y = \frac{c _{1}}{2 ( - 5 x - 2 ) ^{\frac{2}{5}}} - \frac{5}{2}

y = \frac{c _{1}}{2 ( - 5 x - 2 ) ^{\frac{2}{5}}} - \frac{5}{2}

\frac{d y}{d x} y = x^{2} + 8

(ln (y))^{3} \frac{d y}{d x} = x^{3} y, y (1) = e^{2}

\frac{1}{y ^{2}} y^{^{'}} = 2 x

\frac{d y}{d x} = \frac{y ^{2} + 1}{x}, y (\frac{π}{4}) = 1

y^{^{'}} = x^{2} \cdot y^{2}

What is the solution for (dy)/(dx)=(2y+5)/(-5x-2) ?
The solution for (dy)/(dx)=(2y+5)/(-5x-2) is y=(c_{1})/(2(-5x-2)^{2/5)}-5/2