Differential equations Questions

Calculus

Differential equations Solutions

The mess in a restaurant can be measured by M(t). Assume that M(0) = 0, the restaurant starts out each month completely clean. Over time the rate of change in the mess is proportional to (100 M). After 50 hours the restaurant had a mess index of 20. A completely messy restaurant has a value of 100. How many hours does it take for the restaurant to have a mess index of 90? (A) 493.89 (B) 516.27 (C) 523.75 (D) 548.31

Calculus

Differential equations Solutions

Solve the following second order ODE. xy" - cos xy' + sin xy = 0, x>0

Calculus

Differential equations Solutions

Solve the following second order ODE. xy" - cos xy' + sin xy = 0, x > 0

Calculus

Differential equations Solutions

The probabilities of events A, B, and An B are given. Find (a) P(A U B), (b) the odds in favor of and the odds against A, (c) the odds in favor of and the odds against B, and (d) the odds in favor of and against A⋂B. P(A) = 7/10, P(B) = 3/10, P(A⋂B)=0 (a) P(A U B) = (Simplify your answer.) (b) The odds in favor of A are (Simplify your answer. Type whole numbers.) The odds against A are (Simplify your answer. Type whole numbers.) (c) The odds in favor of B are (Simplify your answer. Type whole numbers.) The odds against B are (Simplify your answer. Type whole numbers.) (d) The odds in favor of An B are ☐☐ (Simplify your answer. Type whole numbers.) The odds against An B are: (Simplify your answer. Type whole numbers.)

Calculus

Differential equations Solutions

Determine whether the given equation is exact. If it is exact, solve. (2xy²-3) dx +(4+2x²y)dy=0

Calculus

Differential equations Solutions

4. (20 pts.) A) Find the inverse Laplace transform of the following functions. a.

Calculus

Differential equations Solutions

Solve the initial value problem 4y" - 12y' +9y = 0, y(0) = 3, y'(0) = 5. y(t)=

Calculus

Differential equations Solutions

Solve the initial value problem 4y" - 12y' +9y = 0, y(0) = 3, y'(0) = 5. y(t) = How does the solution behave as t → ∞o?

Calculus

Differential equations Solutions

Solve d²y/dt² = -(1/y³) subject to y(0) = y₀ and y'(0) = 0.

Calculus

Differential equations Solutions

The following table shows the rate of water flow (in L/min) through a dam. t (min) 1 4 7 10 13 16 19 V'(t) (l/min) 1 10 5 6 8 3 8 Approximate the total volume of water that passed through the dam from t=1 to t=19 using Simpson's rule, with n=6.

Calculus

Differential equations Solutions

Use variation of parameters to find a general solution to the differential equation given that the functions y₁ and y₂ are linearly independent solutions to the corresponding homogeneous equation for t> 0. ty" -(t+1)y' +y=3t³; y₁=e^ t, Y₂=t+1 A general solution is y(t) =c₁ e^ t+ c₂(t+1)-3t²

Calculus

Differential equations Solutions

In this problem, let us try to maximize the function J= |3x +2y-7z| under the constraint of 2x² + y² + 3z² =5, by applying the Cauchy-Schwarz inequality. The trick is to view J as the absolute value of the inner product of u̲=(√2x, y, √3z) and u̲= (3/√2,2, -7/√3). Find the maximum value of J.