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Popular >

(dy)/(dx)= 1/2 x+3

Solution

\frac{d y}{d x} = \frac{1}{2} x + 3

Solution

y = \frac{x ^{2}}{4} + 3 x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{2} x + 3

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{1}{2} x + 3

If

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

then

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

y = \int \frac{1}{2} x + 3 d x

\int \frac{1}{2} x + 3 d x = \frac{x ^{2}}{4} + 3 x + c_{1}

y = \frac{x ^{2}}{4} + 3 x + c_{1}

Popular Examples

derivative of xe^t

\frac{d}{d x} (x e^{t})

integral of tan^5(x)sec^{-3/2}(x)

\int tan^{5} (x) sec^{- \frac{3}{2}} (x) d x

integral of x^2sqrt(x^2+9)

\int x^{2} x^{2} + 9 d x

integral of 1/((5x)^2)

\int \frac{1}{( 5 x ) ^{2}} d x

integral of (ln(cos(x)))/((cos(x))^2)

\int \frac{ln ( cos ( x ) )}{( cos ( x ) ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)= 1/2 x+3 ?
The solution for (dy)/(dx)= 1/2 x+3 is y=(x^2)/4+3x+c_{1}