What is the solution for (dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1) ?

The solution for (dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1) is y=(c_{1})/((x^2+1)^{3/2)}+2

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(dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1)

\frac{d y}{d x} + \frac{3 x y}{x ^{2} + 1} = \frac{6 x}{x ^{2} + 1}

y = \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{3}{2}}} + 2

Solution steps

\frac{d y}{d x} + \frac{3 x y}{x ^{2} + 1} = \frac{6 x}{x ^{2} + 1}

Solve separable ODE:

y = \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{3}{2}}} + 2

y = \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{3}{2}}} + 2

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y^{^{'''}} - 5 y^{^{''}} + 3 y^{^{'}} + 9 y = 0

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What is the solution for (dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1) ?
The solution for (dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1) is y=(c_{1})/((x^2+1)^{3/2)}+2