Simplify the problem

Problem Set 2, Part 1 1. y' = (2y4 + x*)/xy³ 2. у 3 2ху/(x? — у?) 3. у'- (x2 + у?)/ху. 4. у - (x?у - у)у + 1), У(3) — -1 5. sin x cos? y dx + cos² x dy = 0

Can you please solve all of these sub problems and show all of the steps

Can you please solve the questions D, E and F and show all of the steps

Kindly solve 4th part and 5th part

a. Solve the initival value problem: y = 5 cos(2r)/(6+ 5y). y(0) = -1. %3! -6+\36 -(10-(- sin(x)+ b. When'solving an ODE, the solution is only valid in some interval. Furthermore, if an initial condition is given, the solution will only be valid in the largest interval in the domain of the solution that is around the a-value given in the initial condition. In this case, since y(0) = -1, then the solution is only valid in the largest interval in the domain of y around a = 0. For the following question, you do not need to find the interval exactly, but you should use a graphing utility, such as WolframAlpha, to plot the solution. Determine where the solution attains its maximum value. That is, you must compute the critical value of y using calculus. Note that there is only one a-value in the largest interval about z 0 that works, which you can determine based on the graph. Terit

Solve Q4

5. solve the ode

5. In determining the particular solution to 2x" + 3x' = 3 sin(1), you must solve 2(-M sin(1) - N cos(t))+ 3(M cos(t) – N sin( t)) = 3sin(t) Is the above equation true if you choose xp = N cos(1) + M sin(t) It is true 919 = 0 It is false 919 = 1 Suppose it is true, calculate 920 = M and 921 = N