1. Given x = r2 cos(20) and y = -r² sin(20)

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: 13. Find y' for sin(xy²) + x² = y². %3D

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Q: 1. 6(x) = e- sin a, for y' + y cos x

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: se the method of undetermined coefficients to find the general solution to: y'' + y = 5 Cos(t)

A: Use the method of undermined coefficient to find the general solutionof differential equationy''+y=5…

Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: 8. Find a particular solution yp(x) to the equation y" +y' – 2y = 5 sin x in the form yp(x) = c1…

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Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

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Q: 4- the solution for the following O.D.E (2xy- sin(x))dx = x²dy- cos(y) dy

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Q: 3- The integration of ſ cos(7x + 5).dx is: (a) cos(7x + 5) + C (b) sin(7x + 5) + C (e)극 sin(7x + 5)…

A: The given integral is, I=∫cos7x+5dx Now, substitute z=7x+5in the above integral,…

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

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Q: 15. For fe' cos x dx, what is du? cos x e' dx - sin x dx G(e* cos x + e" sin x) + C

A: The given question can be solved as shown in step2.

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); u =

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Q: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

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Q: 5) S V2 + sin 3t · cos 3t dt

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Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); U =

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Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

A:

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

A:

Q: 1- The integration of ſ cos . dx is: (a) sin를 + C (b) 2 sin +C coS x (c) 2 cos를+C (d) + C 2

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Q: 9. cos (2t) dt 10. " sin?t cost dt /2 11. sin'x cos?x dx 12. (2 sin0)² d®

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Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

A:

Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

A:

Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: A particular solution for y +2y +y=1-cosX

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Q: dy.xandy in =cos = COS e

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Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: 4 sin (In t) cos`(1nt) dt 5.

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Q: 20. e2= cos(z/4) dz

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Q: 7. Determine the following general antiderivatives. | cos*(x) b. sin(x) xp- 10 10 | sin(x)cos(x)] d.…

A: Please see the below picture for detailed solution.

Q: .4. (c) y = x*; y = sin(Tx/2); about x = -1

A:

Q: 16. Evaluate S x² cos(x³) dx a.) -sin(x³) + C b.) sin(x') + C c.) - sin(x³) + C d.) sin(x') + C

A: