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dy Find the function y(x) satisfying dx = 4x - 9 and y(5) = 0. dy The function y(x) satisfying = 4x - 9 and y(5)= 0 is y(x) = dx
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
[2xy cos (x+y) – sin x) dx + x2 cos (x+y) dy o
(1 point) Solve the following differential equation: (tan(x) 8 sin(x) sin(y))dx + 8 cos(2) cos(y)dy = 0. = constant. help (formulas)
Solve the given differential equation. 9) dy + y = 14 +6 cos 3x 9) dx² B) y = ci sin x + c2 cos A) y=cı sin x +c2 cos x + cos 3x +14 C)y=cı sin x +c2 cos x - cos 3x +14 D) y=q sin x +02 cos x - sin 3x+14
5. (4 points) Calculate integral $.264 + z sin y)dx + (x? cos y − 3yjº)dy along triangle with vertices (0,0), (1,0) and (1,1), oriented counterclockwise, using Green's theorem.
(a) [1[*(2x*y + 4y2) dy dx (b) ["" ["(y cos(x) + 6) dy dx cos [**(buye* * *) ay ox (a) LiS.*r-* log(4) dy dx (-x log(y)) dy dx -Il
Find a solution 6. (e* sin y + tan y)dx + (e* cos y + x(sec y)2)dy = 0.
find a solution 6. (e* sin y + tan y)dx + (e* cos y + x(sec y)2)dy = 0.
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....