What is the solution for (dy)/(dx)=((3y+10507))/(x-12),y(0)=47 ?

The solution for (dy)/(dx)=((3y+10507))/(x-12),y(0)=47 is y=-10507/3-1331/648 (x^3-36x^2+432x-1728)

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(dy)/(dx)=((3y+10507))/(x-12),y(0)=47

\frac{d y}{d x} = \frac{( 3 y + 10507 )}{x - 12}, y (0) = 47

y = - \frac{10507}{3} - \frac{1331}{648} (x^{3} - 36 x^{2} + 432 x - 1728)

Solution steps

\frac{d y}{d x} = \frac{( 3 y + 10507 )}{x - 12}

Solve linear ODE:

y = - \frac{10507}{3} - \frac{1331}{648} (x^{3} - 36 x^{2} + 432 x - 1728)

y = - \frac{10507}{3} - \frac{1331}{648} (x^{3} - 36 x^{2} + 432 x - 1728)

y = arcsec (x)

t \frac{d y}{d t} + 2 y = t^{- 3}

\int_{0}^{π} e^{x} sin (x) d x

x \to + 0 lim (\frac{sin ( x )}{4 x})

1500 x + 3000 (4 x + 3)^{- 1} - 1000

What is the solution for (dy)/(dx)=((3y+10507))/(x-12),y(0)=47 ?
The solution for (dy)/(dx)=((3y+10507))/(x-12),y(0)=47 is y=-10507/3-1331/648 (x^3-36x^2+432x-1728)