What is the solution for (x^2+4)(dy)/(dx)+3xy=x ?

The solution for (x^2+4)(dy)/(dx)+3xy=x is y=(c_{1})/(3(x^2+4)^{3/2)}+1/3

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(x^2+4)(dy)/(dx)+3xy=x

(x^{2} + 4) \frac{d y}{d x} + 3 x y = x

y = \frac{c _{1}}{3 ( x ^{2} + 4 ) ^{\frac{3}{2}}} + \frac{1}{3}

Solution steps

(x^{2} + 4) \frac{d y}{d x} + 3 x y = x

Solve separable ODE:

y = \frac{c _{1}}{3 ( x ^{2} + 4 ) ^{\frac{3}{2}}} + \frac{1}{3}

y = \frac{c _{1}}{3 ( x ^{2} + 4 ) ^{\frac{3}{2}}} + \frac{1}{3}

\int (x - 1)^{4} d x

\int 2 x + 7 d x

x + 1

y^{^{''}} - a y^{^{'}} - b y = 0

\frac{d}{d x} (5 ln (7 - x^{2}))

What is the solution for (x^2+4)(dy)/(dx)+3xy=x ?
The solution for (x^2+4)(dy)/(dx)+3xy=x is y=(c_{1})/(3(x^2+4)^{3/2)}+1/3