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Popular >

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

Solution

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

Solution

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

If

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

then

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

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

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

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

Popular Examples

x^2y^{''}+3xy^'+2y=0,y(1)=0.2,y^'(1)=0.3

x^{2} y^{^{''}} + 3 x y^{^{'}} + 2 y = 0, y (1) = 0.2, y^{^{'}} (1) = 0.3

derivative of cos(sqrt(sin(tan(pix))))

\frac{d}{d x} (cos (sin (tan (π) x)))

laplacetransform 3*sin(3t+2)laplace transform

3 \cdot sin (3 t + 2)

integral of cos(X)

\int cos (X) d X

derivative of x(7x+3^{1/3})

\frac{d}{d x} (x (7 x + 3)^{\frac{1}{3}})

Frequently Asked Questions (FAQ)

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