What is the solution for (dy)/(dx)+0.7x=18.2 ?

The solution for (dy)/(dx)+0.7x=18.2 is y= 1/10 (182x-(7x^2)/2)+c_{1}

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(dy)/(dx)+0.7x=18.2

\frac{d y}{d x} + 0.7 x = 18.2

y = \frac{1}{10} (182 x - \frac{7 x ^{2}}{2}) + c_{1}

Solution steps

\frac{d y}{d x} + 0.7 x = 18.2

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) + 0.7 x = 18.2

Isolate

y^{'} (x) : y^{'} (x) = \frac{182 - 7 x}{10}

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

then

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

y = \int \frac{182 - 7 x}{10} d x

\int \frac{182 - 7 x}{10} d x = \frac{1}{10} (182 x - \frac{7 x ^{2}}{2}) + c_{1}

y = \frac{1}{10} (182 x - \frac{7 x ^{2}}{2}) + c_{1}

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What is the solution for (dy)/(dx)+0.7x=18.2 ?
The solution for (dy)/(dx)+0.7x=18.2 is y= 1/10 (182x-(7x^2)/2)+c_{1}