Find the solution of the following initial value problem using the method for a Bernoulli equation:
Find the solution of the following initial value problem using the method for a Bernoulli equation:...
(24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y(1) = 0 (Bernoulli equation) 18 1 b) y" – 4y - 12y = 3e St, y (0) = , y'(0) - (Hint: use the method of undetermined coefficients) c) (2xy - 9x) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE) = -1 7
solve 5c 5. (24 points) Find the solution of each of the following initial value problems: a) xy' + 3y = x V),y (1) = 0 (Bernoulli equation) 18 b) y" – 4y' – 12y = 3e5, y (0) =- (Hint: use the method of undetermined 7 coefficients) c) (2xy - 9x?) dx + (2y + x2 + 1) dy = 0,y (0) = - 3 (Hint: first show this is an exact DE)
find solution to ivp xy' + 3y = x(sqrt(y)), y(1) = 0, bernoulli equation
Use the method for solving Bernoulli equations to solve the following differential equation. dy dx +3y = e Xy - 8 Ignoring lost solutions, if any, the general solution is y=0 (Type an expression using x as the variable.)
4.6 (20 pts) Solve the initial value problems for the Bernoulli equation. (a) xy+y=x*y; y(1) = 1/4; (b) xy + 3y = rºy?, y(1) = 1/2.
An equation in the form with is called a Bernoulli equation and it can be solved using the substitution which transforms the Bernoulli equation into the following first order linear equation for : Given the Bernoulli equation we have so . We obtain the equation . Solving the resulting first order linear equation for we obtain the general solution (with arbitrary constant ) given by Then transforming back into the variables and and using the initial condition to find ....
Problem 5: Find the general solution to the following differential equation using the method of variation of parameters: x2y"+ xy' + (x2− 1/4 )y = x 3/2 given that the complementary solution on (0,∞) is given by yc = c1x-1/2cos(x) + c2x -1/2sin(x).
4. (18 marks) Find the solution of the following initial value problem for a nonho- mogeneous second order differential equation with constant coefficients: Y" – 3y = 3e36 - 18t2 +4, y(0) = 0, y(0) = 4
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
The objective of this question is to find the solution of the following initial-value problem using the Laplace transform. The objective of this question is to find the solution of the following initial-value problem using the Laplace transform y"ye2 y(0) 0 y'(0)=0 [You need to use the Laplace and the inverse Laplace transform to solve this problem. No credit will be granted for using any other technique]. Part a) (10 points) Let Y(s) = L{y(t)}, find an expression for Y(s)...