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Popular >

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

Solution

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

Solution

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

Graph

Popular Examples

integral of-2/(sqrt(100-9t^2))

\int - \frac{2}{100 - 9 t ^{2}} d t

limit as x approaches-1 of sin((pix)/6)

x \to - 1 lim (sin (\frac{π x}{6}))

integral of 4x^{3/2}

\int 4 x^{\frac{3}{2}} d x

(\partial)/(\partial x)(sqrt(x^2+y^2-5))

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

integral from 0 to pi/2 of cos((2x)/3)

\int_{0}^{\frac{π}{2}} cos (\frac{2 x}{3}) d x

Frequently Asked Questions (FAQ)

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