By applying necessary substitutions, the differential equations to the left will be reduced to the differential equations to the right. Match these differential equations. dy +2e²lny dx=0 (Inx+ Arctany) dx X (Arcsin ²x + tan²y) dx √1-x² Arctany dy 1+y² =0 + Arcsinx tany sec2y dy=0 —em cscr cotx dx – (csc+e cscx}e- dy=0 - 2(x + 1)(x² + y² + 2x - 4y) dx + 2(y-2) (x²-y²=2x+4y) dy=0 A u² du + (uv+v²) dv=0 B. (u+v) du-u dv=0 C. (u+v) du-v dv=0 D. (u²-v²) du+uv dv=0 E. u dv+v² du=0 F. (u+v) dv+(u-v) du=0 G. (u+v) du+ (u-v) dv=0 H. (u²+v²) dv+uv du=0 1. (u²+v²) du+uv dv=0 J. v² du+ (u²+uv) dv=0 K. (u-v) du+v dv=0 L. v² dv+ (u²+uv) du=0 M. (u-v) du- v dv=0 N. (u+v) du-(u-v) dv=0 O. u² dv+v du=0

Q: Solve the differential equation 2 ď²y dy + 4y = cos(ln x)+x sin(ln x), r > 0, dr dr? by using the…

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Q: 18x + 3 2. dx 3x* + 2x 3. J 4y13 r - y' – 4y+3 -dy y+5 4. [[sec(4x) – csc()]dx

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Q: i) Solve the differential equation dx +tan x tan y = cos x secy.

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Q: Given x = sin 7t and y dy/dx = d²y/dx² = = cos 7t, find the following derivatives as functions of t.

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Q: 8. Solve the differential equation (x+y)² dy = a². dx

A: Let x+y=t This implies 1+dydx=dtdx

Q: You are given the following differential equation: d2y/dx2 + 5 (dy/dx) + 6y = 10 cos x Find a…

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Q: 11. The apothem and the height of a regular four-cornered pyramid are 8 cm and 4 cm respectively.…

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Q: Solve the differential equation dy + 2y sin x cos x = 4cosx dx cos?x subject to y = 3 when x = .…

A: The given differential equation is cos2xdydx+2ysinxcosx=4cos5x.....(1) with condition y=3 when x=π6

Q: dx - x = (-²/cost) x³ dt 2t 2

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Q: Solve dy - dx coeff and substituting yp & the derivatives in the Linear Diff Eq. The answer should…

A: According to question,Given differential equation,d 2ydx - 2dydx = ex sin x

Q: dy +x Sin ( 2y) – xe-x Cos ² y = 0 dx

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Q: The 2nd derivative of the given functions is y = 3 cos (4x – 5)

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Q: Find dy/dx by implicit differentiation. 32 y +8yr=-7 dy/dx

A: Given                3x2y+8y2x=-7               we have to find dydx

Q: (2) Solve the differential equation dy sin x, y(0) = 3. dx

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Q: a. Evaluate S dx α x2+βx+13

A: Given- ∫xαx2+βx+13dx To find- The value of the above integral. Identity Used- ∫1a2+x2=1atan-1xa and…

Q: dy = 3 sin (6x - 2y) dx

A: This is a problem of the differential equations.

Q: Solve xdx - x² (cot 2y + x2y cos 2y)dy = 0

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Q: log3 (2r² + y) + tan (2-³) = sin-¹ (²-1) +

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Q: ind the solution of the given differential equation: cos 2y 3xy?) dæ + (cos 2y – 2xsin2y 2x' y) dy =…

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Q: y = eVx+cosx

A: To  findderivative of1)y=ex2+cosx

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given