What is the solution for (1+x^2)(dy)/(dx)+3xy=5x ?

The solution for (1+x^2)(dy)/(dx)+3xy=5x is y=(c_{1})/(3(x^2+1)^{3/2)}+5/3

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(1+x^2)(dy)/(dx)+3xy=5x

(1 + x^{2}) \frac{d y}{d x} + 3 x y = 5 x

y = \frac{c _{1}}{3 ( x ^{2} + 1 ) ^{\frac{3}{2}}} + \frac{5}{3}

Solution steps

(1 + x^{2}) \frac{d y}{d x} + 3 x y = 5 x

Solve separable ODE:

y = \frac{c _{1}}{3 ( x ^{2} + 1 ) ^{\frac{3}{2}}} + \frac{5}{3}

y = \frac{c _{1}}{3 ( x ^{2} + 1 ) ^{\frac{3}{2}}} + \frac{5}{3}

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

\int x arctan (20 x) d x

\frac{x}{x ^{2} - 2}

\int (3 x^{2} + 5) cos (7 x) d x

x^{7} \cdot e^{x}

What is the solution for (1+x^2)(dy)/(dx)+3xy=5x ?
The solution for (1+x^2)(dy)/(dx)+3xy=5x is y=(c_{1})/(3(x^2+1)^{3/2)}+5/3