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Popular >

(dy)/(dx)(x+1)=x+6

Solution

\frac{d y}{d x} (x + 1) = x + 6

Solution

y = 5 ln (x + 1) + x + c_{1}

Solution steps

\frac{d y}{d x} (x + 1) = x + 6

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) (x + 1) = x + 6

Isolate

y^{'} (x) : y^{'} (x) = \frac{x + 6}{x + 1}

If

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

then

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

y = \int \frac{x + 6}{x + 1} d x

\int \frac{x + 6}{x + 1} d x = 5 ln (x + 1) + x + c_{1}

y = 5 ln (x + 1) + x + c_{1}

Popular Examples

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\int \frac{1}{8 x + 1} d x

integral of (5x^2-x-3)/(x^2(x+1))

\int \frac{5 x ^{2} - x - 3}{x ^{2} ( x + 1 )} d x

limit as x approaches 0+of x^2(ln(x))

x \to 0 + lim (x^{2} (ln (x)))

derivative of sec(x-pi/4)

\frac{d}{d x} (sec (x - \frac{π}{4}))

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)(x+1)=x+6 ?
The solution for (dy)/(dx)(x+1)=x+6 is y=5ln(x+1)+x+c_{1}