What is the solution for (dy)/(dx)=log_{10}(x) ?

The solution for (dy)/(dx)=log_{10}(x) is y=xlog_{10}(x)-x/(ln(10))+c_{1}

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(dy)/(dx)=log_{10}(x)

\frac{d y}{d x} = lo g_{10} (x)

y = x lo g_{10} (x) - \frac{x}{ln ( 10 )} + c_{1}

Solution steps

\frac{d y}{d x} = lo g_{10} (x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = lo g_{10} (x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int lo g_{10} (x) d x

\int lo g_{10} (x) d x = x lo g_{10} (x) - \frac{1}{ln ( 10 )} x + c_{1}

y = x lo g_{10} (x) - \frac{1}{ln ( 10 )} x + c_{1}

Simplify

y = x lo g_{10} (x) - \frac{x}{ln ( 10 )} + c_{1}

\frac{d y}{d x} = \frac{x ^{9} - 8 y}{x}

\int_{6}^{12} 2 x - 18 d x

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

y^{^{''}} + y = e^{x}

\frac{d y}{d x} = \frac{( x ^{2} - 1 )}{2 y}, y (3) = 1

What is the solution for (dy)/(dx)=log_{10}(x) ?
The solution for (dy)/(dx)=log_{10}(x) is y=xlog_{10}(x)-x/(ln(10))+c_{1}