What is the solution for x*(dy)/(dx)+7y= 1/x ?

The solution for x*(dy)/(dx)+7y= 1/x is y= 1/(6x)+(c_{1})/(x^7)

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x*(dy)/(dx)+7y= 1/x

x \cdot \frac{d y}{d x} + 7 y = \frac{1}{x}

y = \frac{1}{6 x} + \frac{c _{1}}{x ^{7}}

Solution steps

x \cdot \frac{d y}{d x} + 7 y = \frac{1}{x}

Solve linear ODE:

y = \frac{1}{6 x} + \frac{c _{1}}{x ^{7}}

y = \frac{1}{6 x} + \frac{c _{1}}{x ^{7}}

\int e^{5 x} sin (5 x) d x

y = cos (x), x = \frac{π}{4}, x = \frac{π}{3}

\frac{d y}{d x} + y = 0

\int \frac{1}{x ( 1 + x )} d x

\frac{\partial}{\partial x} (2^{x})

What is the solution for x*(dy)/(dx)+7y= 1/x ?
The solution for x*(dy)/(dx)+7y= 1/x is y= 1/(6x)+(c_{1})/(x^7)