Solve the following initial-value problems (which could be homogeneous, Bernoulli, or exact). (2x2 + y2) dx...
determine which equations are exact and solve them 10. (2x2 + 8xy + y2) dx + (2x2 + xy3/3) dy = 0
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)
(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
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
Solve the following exact differential equation with initial value. (5x + 4y)dx + (4x - 8y3)dy = 0, y(0) = 2
Solve the initial value problem (2x – y2)dx + (1 – 2xy)dy = 0, y(1) = 5
Solve the initial value problem Please show step by step (c) (x + y)dx - (x - y)dy = 0, y(1) = 0 (d) xy' - y2 in x + y = 0, y(1) = 2
Solve A,B,C,D step by step please 2.- Obtain the general solution of the following homogeneous differential equations A. y dx - (2x2 + 3xy)dy = 0 B. y' y2- 3xy C. y(In y2 – In x2 + 1)dx – xdy = 0; y(1) = e" D. y' = (x+y-1,; y(0) = 1
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.)
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...