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

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

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(dy)/(dx)+y/(x+2)=5(x-2)y^{1/2}

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

y = x^{4} + 4 x^{3} + 2 c_{1} x (x + 2)^{\frac{1}{2}} + 4 x^{2} + \frac{- 84 x ^{4} - 308 x ^{3} + 168 x ^{2} - 84 c _{1} x ( x + 2 ) ^{\frac{1}{2}} + 1680 x - 168 c _{1} ( x + 2 ) ^{\frac{1}{2}} + 9 c _{1}^{2} + 1568}{9 x + 18}

Solution steps

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

Solve Bernoulli ODE:

y = x^{4} + 4 x^{3} + 2 c_{1} x (x + 2)^{\frac{1}{2}} + 4 x^{2} + \frac{- 84 x ^{4} - 308 x ^{3} + 168 x ^{2} - 84 c _{1} x ( x + 2 ) ^{\frac{1}{2}} + 1680 x - 168 c _{1} ( x + 2 ) ^{\frac{1}{2}} + 9 c _{1}^{2} + 1568}{9 x + 18}

y = x^{4} + 4 x^{3} + 2 c_{1} x (x + 2)^{\frac{1}{2}} + 4 x^{2} + \frac{- 84 x ^{4} - 308 x ^{3} + 168 x ^{2} - 84 c _{1} x ( x + 2 ) ^{\frac{1}{2}} + 1680 x - 168 c _{1} ( x + 2 ) ^{\frac{1}{2}} + 9 c _{1}^{2} + 1568}{9 x + 18}

y = 4 x - 3 x^{2}

\int \frac{1}{x ( x ^{3} - 1 )} d x

n = 1 \sum \infty \frac{2}{π ^{n}}

\int \frac{x ^{5}}{5} d x

x \to \infty lim (\frac{4 ^{x}}{3 ^{x - 1}})

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