Solve the given initial-value problem. dx dt -9x - y dy 16x - y dt x(1) = 0, y(1) = 1 = x(t) e-5(t-1) -5 (t+1) + te = y(t) = (4t - 3)e5-5t

Q: find dy/dx at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Given that  (x + 2)2 − 6(2y + 3)2 = 3 Differentiating with respect to x

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: 2/7,545

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Q: You are given a first-order D.E. = x2 + y³ . Suppose the solution y(x) satisfies the initial dx…

A: dydx=x2+y3  and y1=-1

Q: find dy/dt.

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Q: dy =x+3x + e2x dx 1. Solve the initial value problem when x-0. y-2.

A: The given differential equation is solved by variable separable method.

Q: (x5 + 3y)dx - x dy = 0

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Q: dy - 6/7 = 3x dx and y(- 1) = - 3. Find the function y(x) satisfying The function y(x) satisfying dy…

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Q: Find a general solution of (D² +4)(D – 1)(D + 3)²y(x) = 0. 1. D shows the derivative operator.

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Q: for the implicit equation zey +In(y) = x³-12? da dy 3x2 02-2 = xey + Y 3x² - ey dy da xey + What is…

A: Topic = Derivative

Q: Solve the initial value problem: x2 dx + 2ydy = 0,  y(0) = 2

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Q: Find and classify the stationary points of the function 1 G(x, y) = 3x² + xy - 2y² - 2x + 4y - 1

A: Given function is .For stationary points .Now, or, And or, To eliminate y from (1) and (2),…

Q: A dog is walking in a straight line on the road looking for bones. The dog is attracted to the smell…

A: The function x(t) indicates the position of dog with respect to time, t. So, the velocity of dog is…

Q: Solve the initial value problem: (3x + 8)(y² + 4)dx – 4y(x² + 5x + 6)dy = 0, y(1) = 2

A: A differential equation is said to be in separable form if it can be written in the form . Such a…

Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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Q: t² - t dt 0, = (x)6 g'(4) =

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Q: g(x) g'(5) = 2 X 13 1+t2 dt

A: Given query is to find indicated derivative.

Q: dy (d) 3y(x2 – 1) + (x³ + 8y – 3x) dx 0 =

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Q: Find the solution to the initial value problem: x2dy = 2y dx y(x) = y(1) = -2

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Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: Solve the initial value problem: (2ye2xy – 2) dx + (2xe2*y +) dy = 0; y(1) = 1 %3D y²

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Q: Show that both R and R2 may be covered by countably many open balls.

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Q: Solve the initial value problem: dy x(1+ y)²; y(0) = –3 dx

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Q: Solve (x − y − 1) dy − (x + 3y − 5) dx = 0

A: Given: x-y-1dy-x+3y-5dx=0

Q: : Solve-Using D-operator dy dx + 3y – 5x - e-t = 0 dt %3D dt dx dy 2- dt +x +y-3 = 0 dt

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Q: solve this D.E using separation of variables dy/dx = (xy+3x-y-3)/(xy -2x+4y-8)

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Q: dy dx 3x² + 4x + 2 2(x - 1) y(0) = -1. . Check if it has a unique solution in some interval about x…

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Q: 4-3x Consider the function y=e¹-3. Find y'.

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