--- T2-1 (20 Points): Find the P.S. of the IVP: x2 + 2xy + y2 1+ (x + y)2 y(x = 0) = 4 Primes denote derivatives WRT X.
T2-1 (20 Points): Find the P.S. of the IVP: x2 + 2xy + y2 1 + (x + y)2 y(x = 0) = 4 Primes denote derivatives WRT x. Sy' T2-2 (20 Points): Find the G.S. of the DE: xy' + y = 3x2 Prime denotes derivative WRT x. (Hint: guess a P.S. yı = Axa)
I need help with question's 1 and 2 T2-1 (20 Points): Find the P.S. of the IVP: x2 + 2xy + y2 y = 1+ (x + y)2 y(x = 0) = 4 Primes denote derivatives WRT X. T2-2 (20 Points): Find the G.S. of the DE: xy' + y = 3x2 Prime denotes derivative WRT x. (Hint: guess a P.S. Yı = Ax")
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
QUESTION 2 Calculate and simplify det if f(x,y) = O x2 - y2 + 2xy (x2 + y2)2 O 4x(+- x² + 3y2) (x² + y²)3 o 4x(x² – 3y?) (x² + y²)3 OO O x2 - y2 + 2xy (x² + y²)?
Show that if x and y are real numbers, x2 + y2 >= 2xy and (x + y)2 >= 4xy; When does equality hold (with proof)? Show that if x and y are real numbers, x2 + y2 2xy and (x y) 2Hry. When does equality hold (with proof)?
f(x, y) = x2 + y2 + 2xy + 6. 1- Find all the local extremas and 2) does the function f have an absolute max or min on R2
Find the general solution of x2 y' = y2 + 2xy
1. Find lim(x,y)=(1,1) x2-y2 2xy 2. Show that lim(x,y)-(0,0) 21 z does not exist 3. Show that lim(x,y)=(0,0) z?”, does not exist 4. Find lim(x,y)=(0,0) eye if it exists, or show that the limit does not exist
Find the solution of the IVP (3x^2 + y^2) + (2xy + cos y) y' =0 ; y(2)=0