show the ivp is an exact de and then solve (2xy - 9x^2)dx + (2y +...
solve the given de or ivp 3. [2xy cos (x²y) - sin x) dx + rcos (2²y) dy = 0.
solution for all 4 please 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 – x sin y – 2y) dy = 0. 1 dy 2. + cos2 - 2.cy y(y + sin x), y(0) = 1. + y2 dc 3. [2xy cos (2²y) – sin x) dx + x2 cos (x²y) dy = 0. (1+y! x" y® is...
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)...
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
Determine whether the equation is exact. If it is, then solve it (2xy + 3)dx + (x²-6) dy=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The equation is exact and an implicit solution in the form F(x,y)=Cis-C, where is an arbitrary constant (Type an expression using x and y as the variables.) OB. The equation is not exact,
4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)dy 0 4. Solve the exact differential equation. (1-2xy)dx + (4y3 - x2)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)
solve using Exact and Non-Exact DE 13. -y dx +(x - x) dy 0 dy 0