Determine the following ODES. (2xy)dx + 2y² dy = 0, y³ dx + 3x³y² dy = 0 G) (cot y)y' =-1 (y + cos x)dx + (x + sin y)dy = 0 (2y² – 4x + 5)dx + (4 – 2y + 4xy)dy = 0 (y – (x + y)²)dx + ((x + y)² – x)dy = 0 (y + x*y²)dx + 2x dy = 0, e*(x + 1)dx + (ye♥ – xe*) dy = 0, (2xy)dx + 2y² dy = 0, y' = e2x + y – 1 (x + sinx + siny)dx + cosy dy = 0,

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A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

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Q: (sin 2x)y' = y cos 2x

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A: I am attaching image so that you understand each and every step.

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Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

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A: This integral can be solved by changing the order of the integral. The order can be changed by…

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Q: Find general solution of ODE : y'+y=sinx+x

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Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: 7. (a) Find dy/dx, when x = a(1 + cos 0), y = a (0 + sin 0). (b) Differentiate xcosx w. r. t.…

A: Differentiation using Logarithms: When a function appears as an exponent of another function we make…

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Q: 1. y = (3x² + 3x - 1)4 2. y = (5-2x)-2 3. y = cos3 (πx)

A: Disclaimer: Since you have posted a question with multiple questions, we will solve the first three…

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A: Proceed as shown below...

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A: Differential

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A: Explanation of the answer is as follows

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: Intergrate dy (2y-x) =In Co)

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

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Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

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Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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Q: If f(2, y) = 3 sin(2x +y) - 4 cos(z- y) then the second derivative f is %3D a. -12 sin (2x +y) +4…

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