Differential Equations Answers

dy/dx= y(xy^(5) − 1)

2. Solve by variation of parameters:

(D ^ 2 - 2D + 1) * y = x ^ (3/2) * e ^ x

1. Solve the ordinary linear differential equation by the method of undetermined coefficients: y'' -2y' -3y=2e^ 4x

2. Solve by variation of parameters:

(D ^ 2 - 2D + 1) * y = x ^ (3/2) * e ^ x

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -" ____ x² + "\\sqrt[4]{x}"

Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially, there are 250 strands of the bacteria in the solution which grows to 800 strands after seven hours. Find (a) an expression for the approximate number of strands in the culture at any time t and (b) the time needed for the bacteria to grow to 1600 strands. 

A tank contains 100 gal of brine made by dissolving 60 lb of salt in water. Salt water containing 1 lb of salt per gallon runs in at the rate of 2 gal/min and the well-stirred mixture runs out at the same rate of 3 gal/min. Find the amount of salt in the tank after 30 minutes. 

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -" ____ x² + "\\sqrt[4]{x}"