6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w = xy.

dz Find from the equation x*y+ x z+ z² = 4 ax

1. (2x3у2 + 4x?у+ 2хy? + ху* + 2у)dx + 2(y3 + x?у+x)dy %3D 0 2. у? dx + (x2 — ху — у?)dy %3D 0 3. у(2ху + 1)dx +x(1 + 2ху — х3у3)dy %3D 0 4. x(4ydx + 2xdyу) + у3 (Зуdx + 5xdy) 3D 0 5. (2xye**y + y?e*y² + 1)dx + (x²e**y + 2xye*y² – 2y)dy = 0 6. cscetan@dr- (rcsc@ + tan?Ө)dӨ 3 0

1. (a) Consider the matrix A (ii) det ([20 Compute the determinant of the matrix and find all values of t, if any, such that A is invertible. Indicate all the steps in your calculations. (b) Let 3g 3h 2a+d 2b+e 2c + f 5a 5b 1 0 6 2 t t 13 48 8 20 22 3i A 5c - and let det (A) = 6. Find the following determinants: (i) det (((3.4)²)¹) 1) Indicate all the steps in your calculations. a d 9 9 b e ƒ h teR.