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Popular >

(dy)/(dx)= 1/2 x+1

Solution

\frac{d y}{d x} = \frac{1}{2} x + 1

Solution

y = \frac{x ^{2}}{4} + x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{2} x + 1

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{2} x + 1

If

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

then

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

y = \int \frac{1}{2} x + 1 d x

\int \frac{1}{2} x + 1 d x = \frac{x ^{2}}{4} + x + c_{1}

y = \frac{x ^{2}}{4} + x + c_{1}

Popular Examples

area f(x)= 1/x ,g(x)= 1/3 ,[2,5]area

f (x) = \frac{1}{x}, g (x) = \frac{1}{3}, [2, 5]

derivative of (7u^2)/((u^2+u)^3)derivative of

\frac{7 u ^{2}}{( u ^{2} + u ) ^{3}}

integral of (3x^2)/(sqrt(1-x^6))

\int \frac{3 x ^{2}}{1 - x ^{6}} d x

area x,x^2-2 area

x, x^{2} - 2

limit as x approaches 0 of 3cos(x)

x \to 0 lim (3 cos (x))

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)= 1/2 x+1 ?
The solution for (dy)/(dx)= 1/2 x+1 is y=(x^2)/4+x+c_{1}