Solve: \(\frac { dy }{ dx } \) = sin(x + y)

Solve: x²\(\frac { dy }{ dx } \) = y²+2xy given that y = 1, when x = 1

Solve: (y-x)\(\frac { dy }{ dx } \) = a²

Solve: (D² + 14D + 49)y = e^-7x + 4.

The net profit p and quantity x satisfy the differential equation \(\frac { dp }{ dx } =\frac { 2{ p }^{ 3 }-{ x }^{ 3 } }{ 3x{ p }^{ 2 } } \). Find the relationship between the net profit and demand given that p = 20, when x = 10.

The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation \(\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } } \). Find the relationship between c and q if c = 1 when q = 1.

The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x²+2y²)dx-(x²+4xy)dy = 0. What is the relation between total cost and output if y = 2 when x = 1?

Equipment maintenance and operating costs (are related to the overhaul interval x by the equation \({ x }^{ 2 }\frac { dc }{ dx } -10xc=-10\) with c = c₀ and x = x₀. Find c as a function of x.

Suppose that the quantity needed Q_d = 42 -4p-4\(\frac { dp }{ dt } +\frac { { d }^{ 2 }p }{ { dt }^{ 2 } } \) and quantity supplied Q_s = -6 + 8p where p is the price. Find the s equilibrium price for market clearance.

The net profit p and quantity x satisfy the differential equation \(\frac{d p}{d x}=\frac{2 p^{3}-x^{3}}{3 x p^{2}}\). Find the relationship between net profit and demand given that p = 20, when x = 10.

The rate of increase in the cost c of ordinary and holding as the size q of the order, increase is given by the differential equation \(\frac{d c}{d q}=\frac{c^{2}+2 c q}{q^{2}}\). Find the relationship between x and q if c = 1, when q = 1.

The total cost of production y and the level of output x are related to the marginal cost of production by the equation (6x² + 2y²) dx - (x²+ 4xy) dy = 0. What is the relation between total cost and output if y = 2, when x = 1

Solve : \( \frac{d y}{d x} =\frac{y}{x}-\frac{y^{2}}{x^{2}} \)

The rate of increases in the cost c of ordinary and holding as the size of the order q increases is given by the differential equation \(\frac{d c}{d q}=\frac{c^{2}+q^{2}}{2 c q}\). Find the relationship between c and q if c = 4 and q = 2.

The total cost of production y and level of output x are related to marginal cost of production by the equation \(\frac{d y^{\prime}}{d x}=\frac{24 x^{2}-y^{2}}{1 y}\). what is the total cost function of y = 4, when x = 2.