(x – y* + y? sin )dx - (3xy + 2y cos r)dy subject to initial condition y(0) = 1 (M

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: Find dy. y = tan H 4 X + cos(4x)

A:

Q: 6. Find Sin 5x (b) y = THcos 5x dx

A:

Q: Given y = 5e³ + sin(x), OOOO 2.667e³-cos(x) 15e³ + cos(x) 15e³ - sin(x) dy dx 5e³ + cos(x)

A:

Q: dy dx cos(x + y) = 3x Find dy dx dy dx dy dx dy dx = = -3 csc (x + y) - 1 = -3 cos(x + y) - 1 = −3…

A: we need to find out the derivative.

Q: y" + 9y = e²* sin(x)

A:

Q: y = tan (5t - 21 +1)

A:

Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: 5. Find (b) y = cos (11x + 5x).

A:

Q: 1 +(x/y − sin y)y′ = 0

A: 1 +(x/y − sin y)y′ = 01 +(x/y − sin y)dy/dx = 0dx +(x/y − sin y)dy = 0Here M(x,y) = 1 and N(x,y) =…

Q: y′′ + 16y = 32 cos(4x) − 24 sin(4x)

A: The given differential equation is        y'' + 16y = 32cos(4x) − 24sin(4x)…

Q: cos(t)y'-tsin(t) = y ; is this seperable or non-seperable?

A: It can be shows that it is not separable. See the next step

Q: Show that y sin x is a solution to xy" + (2 secx)y' + xy = 2. =

A: