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Popular >

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

Solution

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

Solution

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

Solution steps

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

Let

y

be the dependent variable. Divide by

d x

:

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

Isolate

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

If

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

then

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

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

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

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

Graph

Popular Examples

derivative of x/(x-3-arcsec(2x))

\frac{d}{d x} (\frac{x}{x - 3} - arcsec (2 x))

limit as x approaches 0 of x/(tan(x))

x \to 0 lim (\frac{x}{tan ( x )})

25y^{''}-40y^'+16y=0

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0

integral of cos^2(x)sin^2(x)

\int cos^{2} (x) sin^{2} (x) d x

(2y^2+3xy)+(2xy+x^2)y^'=0

(2 y^{2} + 3 x y) + (2 x y + x^{2}) y^{^{'}} = 0

Frequently Asked Questions (FAQ)

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