Ind. Dep. Type Order Linear Degred Var. No DE. Var. o DE yes I 1 yxy x* Uxx + 5u uy = 5x?uyy 3. y'"+x(y')2 = sinx 4. ex wtt + t2 wx = sin(x) w y" +y' + siny = x 9. y'2 +xy = sinx %3D (y")3 + (y')2 + y = 3 7. amed 2.

Q: 1. Find y'. y = x² In(tan-1(2x))

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Q: Determine and of y = (5r - })(cos z + In z

A: Consider y=5x2+32sin x+ln x. Calculate: dydx=y'. Apply product rule of derivative:…

Q: Calculate value for  sin((j*pi)/2)

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Q: sin(x+y) = y + 2cosx

A: We have to find dydx.                                   sinx+y=y+2cosx

Q: 13. Find mzEDC. (9x- 1)° EE C. A (2r + 13) D

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Q: dx xVx -1 6.

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Q: 7. Let y = tan (3x - 2), find y'.

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Q: Find the derivative. 1 y = _x3 + 3x + Væ 2 Ody dx O Ody dx || ip O 32 y=2x2 +3 + 2x 32 || 2 X +3+1/x…

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: Find y' if y = 5x sin x. O A. y' = - 10 cos x+ 5x sin x B. y" = 10 cos x- 5x sin x C. y' = - 5x sin…

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Q: QIFind dx /1+x²/3

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Q: Differentiate. y= In [(x+7)* x + 8)®(x +2)°] dx

A: Given y = ln(x+7)4(x+8)6(x+2)3

Q: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

A: Sinhu.Coshv =1/2 [Sinh (u+ v) + Sinh (u- v)]

Q: dy Solve x cosy = 2x. (siny) – 1 dx O a. y = arcsin(- + cx²) O b. y = arcsin(; + cæ²) O c. y =…

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Q: Differentiate:

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Q: sinh (u + v)= sinh u. cosh v+ cosh u. sinh v и.

A: Consider the Identities for hyperbolic functions and expand the given expression.…

Q: 15. sin x + cos y = sin x cos y

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Q: 2sim x-1 -y = COST+2

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Q: EX/ find (dy) for function y= banx + — — ban²³x bản dx H-W EX/ find dy for function y = T+ Cost Sinx…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.