Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial...

Obtain an implicit solution of the initial value problem. I've tried integrating a couple of different ways but I wasn't able to find a way to to get "S" where one wasn't in log form and the other was not.

See Answer Question: Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y'' + y = f (t), y (0) = 1, y' (0) = 0, where f (t) = 1, 0 ≤ …

Question: Solve the initial value problem below using the method of Laplace transforms.y''+8y'+12y=42et,y (0)=-5,y' (0)=24Click here to view the table of Laplace transforms.Click …

Step 1 Consider the initial value problem d y d t y = 1, y (0) = 0. The objective is to solve the given initial value problem using ...

A model for the population P (t) in a suburb of a large city is given by the initial-value problem dP dt = P (10 −1 − 10 −7 P), P (0) = 4000, where t is measured in months. Find the population P of the suburb …

Question: Use the Laplace transform to solve the given initial-value problem. y' + 3y = e6t, y (0) = 2 y (t) = Use the Laplace transform to solve the given initial-value problem.

Question: Proceed as in Example 3 of Section 4.10 and obtain the first six nonzero terms of a Taylor series solution, centered at 0, of the given initial-value problem y" = x + y2, y (0) = 1, y" (0) = 1 Use a …

Question: Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem. 4y'-6exy = 0; y (O)= 5 y (x)=+ (Type an expression that includes all terms up to order …

Question: Consider the initial value problem y' +2/3y=1- (1/2t), y (0)=y0. Find the value of y0 for which the solution touches, but does not cross, the t-axis