Solve the differential equation xy' - 2y = 6x? In x. Put the equation into standard form, y' + P(x)y = Q(x). To put the given equation into standard form, divide by x to obtain 2 2 y'-y = 6x In x, so that P(x) = To solve the linear equation, y' + P(x)y = Q(x), multiply both sides by the integrating factor P(x)dx and integrate both sides. v(x) = Now find the integrating factor v(x) = JWA, where P(x) = - so v(x) is as simple as possible. Use a constant of integration C X dx v(x) = e = e - 2 In x Multiply through by v(x) = 1 (6x In x). How? 2 6 In x Simplify to obtain The form of the equation becomes (v(x) • y) = v(x)Q(x). dx Now the left side is dx y so integrate both sides to obtain = 3( In x) + Cwhere C is the constant of integration
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
Please attached image for question. I cant figure out how it uses the equation to obtain solution. Please show steps on how the solution is achieved. Thank you for the help.
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