What is the solution for y^'-1/x y=9,y(1)= 1/7 ?

The solution for y^'-1/x y=9,y(1)= 1/7 is y=9xln(x)+x/7

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y^'-1/x y=9,y(1)= 1/7

y^{^{'}} - \frac{1}{x} y = 9, y (1) = \frac{1}{7}

y = 9 x ln (x) + \frac{x}{7}

Solution steps

y^{'} (x) - \frac{1}{x} y = 9

Solve linear ODE:

y = 9 x ln (x) + \frac{x}{7}

y = 9 x ln (x) + \frac{x}{7}

\int \frac{1}{( 1 + \frac{x}{2} ) ^{2}} d x

\frac{d}{d x} (x^{3} - 5 x)

\frac{d}{d x} ((1 - x) (x^{2} - 2)^{2})

x \to - 1 + lim (\frac{5}{x + 1})

y = csc (x) (x + cot (x))

What is the solution for y^'-1/x y=9,y(1)= 1/7 ?
The solution for y^'-1/x y=9,y(1)= 1/7 is y=9xln(x)+x/7