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Popular >

(dy)/(dx)= 1/2 x+4

Solution

\frac{d y}{d x} = \frac{1}{2} x + 4

Solution

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

Solution steps

\frac{d y}{d x} = \frac{1}{2} x + 4

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{2} x + 4

If

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

then

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

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

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

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

Popular Examples

(dy)/(dx)+xy= x/(y^3)

\frac{d y}{d x} + x y = \frac{x}{y ^{3}}

integral of 7/(x^2-6x+25)

\int \frac{7}{x ^{2} - 6 x + 25} d x

area x^2+2x,1,2 area

x^{2} + 2 x, 1, 2

integral from-2 to 2 of (16)/(x^2-4x-60)

\int_{- 2}^{2} \frac{16}{x ^{2} - 4 x - 60} d x

y^{^{'''}} + y^{^{'}} = x

Frequently Asked Questions (FAQ)

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