What is the solution for (7x+2y)(dy)/(dx)=-2x-7y ?

The solution for (7x+2y)(dy)/(dx)=-2x-7y is y=(-7x+sqrt(45x^2+c_{1)})/2 ,y=(-7x-sqrt(45x^2+c_{1)})/2

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(7x+2y)(dy)/(dx)=-2x-7y

(7 x + 2 y) \frac{d y}{d x} = - 2 x - 7 y

y = \frac{- 7 x + 45 x ^{2} + c _{1}}{2}, y = \frac{- 7 x - 45 x ^{2} + c _{1}}{2}

Solution steps

(7 x + 2 y) \frac{d y}{d x} = - 2 x - 7 y

Solve exact ODE:

y = \frac{- 7 x + 45 x ^{2} + c _{1}}{2}, y = \frac{- 7 x - 45 x ^{2} + c _{1}}{2}

y = \frac{- 7 x + 45 x ^{2} + c _{1}}{2}, y = \frac{- 7 x - 45 x ^{2} + c _{1}}{2}

x \to 2 + lim (\frac{x + 4}{x - 2})

x \to 0 lim (\frac{7 x}{∣ x ∣})

x \to 1 - lim (ln (x^{2} - 1))

x \to 6 + lim (\frac{7}{x - 6})

\int_{0}^{7} 2 t^{2} - 20 t + 48 d t

What is the solution for (7x+2y)(dy)/(dx)=-2x-7y ?
The solution for (7x+2y)(dy)/(dx)=-2x-7y is y=(-7x+sqrt(45x^2+c_{1)})/2 ,y=(-7x-sqrt(45x^2+c_{1)})/2