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

Solve the following Bernoulli equations: a) x2y' + 2y = 2e1/xy1/2 answer: y = e2/x(c-1/x)2 b)...
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
1. Solve the following differential equations: a. xy'=y+Vxy x+2y+3 y'= b. 2x – y +5 x+2y+3 y'= x+2y+5 y cos(x+y)+x+y d. sin(x + y) + y cos(x+y)+x+y C. y'=
Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
Solve the given differential equations:
х 1. y' = y(0) = -2 y+x2y 2. 3x²y dx – (x3 + y3)dy = 0 , y(1) = -2
Which of the following is solution for (x^2 + y^2) dx +2xydy= 0? xy^2+1/3x^3=c x^2y+1/3x^3=c xy^2+1/2x^3=c x^2y+1/2x^3=c
exact differential equations
2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
Systems of Equations: 3x + y = 6 2x-2y=4 Substitution: Elimination: Solve 1 equation for 1 variable. Find opposite coefficients for 1 variable. Rearrange. Multiply equation(s) by constant(s). Plug into 2nd equation Add equations together (lose 1 variable). Solve for the other variable. Solve for variable. Then plug answer back into an original equation to solve for the 2nd variable. y = 6 -- 3x solve 1" equation for y 6x +2y = 12 multiply 1" equation by 2 2x...
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).
Question 2 Solve the given systems of equations by the method of substitution. Note: NO MARKS will be given for using the wrong method. A. x2y + 1 2x-3y 4 B. 3x+y 1 3x-2y 16