Solve the Bernoulli equation
a) xy′−4y = x^2√y,
b) y′ = y(y^3 cosx +tgx),
Solve the exact equation
a) 2xcos^2 ydx +(2y−x2sin2y)dy = 0,
b) (x^3 −3xy^2 +2)dx−(3x^2y−y^2)dy = 0,
PLEASEEE it would mean a world to me
In first question (b) the question is incorrect as it contains a term tgx
Solve the Bernoulli equation a) xy′−4y = x^2√y, b) y′ = y(y^3 cosx +tgx), Solve the...
1: The equation dy + 2y = xy-2 is an example of a Bernoulli equation. (a) Show that the substitution v = y; reduces eqauation to do + 6u = 3x. (b) Find the general solution to the equation in part(a).
please determine which equations are exact and solve them. Exact Equation nice* (x + y + 2xy2 ) + 6x) dx +(2x+ye* +2 ) dy = 0 2) · (3x” cos xy - x® y sin xy + 4x )dx +(8y - x' sin xy) dy = 0
Diff Eq. please tell me equations and process used. explain. Solve: (4y-2x-8)dy_ (3x-y-3)dr xy(dr-dy) l. Solve: (4y-2x-8)dy_ (3x-y-3)dr xy(dr-dy) l.
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)
Question Solve the following Bernoulli D. Eq dy +=y=-x? cos xy? dx x
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
Solve the IVP (for the Bernoulli equation): dy/dx − (1/x)y = 1/y , y(1) = −3
(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 the following Bernoulli equations: a) x2y' + 2y = 2e1/xy1/2 answer: y = e2/x(c-1/x)2 b) xy' + y = x4y4 y(1) = 1/2 answer: y = 1/x(11-3x)1/3
(1 point) A Bernoulli differential equation is one of the form dy dc + P(x)y= Q(x)y" Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u = yl-n transforms the Bernoulli equation into the linear equation du dr +(1 – n)P(x)u = (1 - nQ(x). Consider the initial value problem xy + y = 3xy’, y(1) = -8. (a) This differential equation can be written in the form (*)...