solve diffrential equations: 5-9 1) xy = y to(lny) 2) t (y-1)dt +y (t+1)dly = 31 x²yy¹ - e² = 0 41 yen- x ²nndy== 5)√₁7y² dx -y(1+x²) cy=0 6) Sinx dx-2y dy =0 7) (1+y)² Y(0)=1 = dx 1-X 8) ²³ (x²+2x+1)= -(xy+ y) y' 9₁ y₁= x² +1 + xy² + y² ادار Y(I) = 0

Q: 3- y = sec x prove that d? y + y = 2y3 dx2

A: We have to prove the given differential equation to be true.

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Q: Find f'co) if fco)= (Since\ %3D

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Q: 3) у %3D 2u* + 1 x = 5u? – 5u -

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Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: A local target store bought 116 pizzas at Pizza Hut for its holiday party. Each guest ate 1/6 of a…

A: Let x be the number of pizzas bought by the store and y be the number of guests target have for the…

Q: Solve csc y dx + sec²x dy = 0 elect one: a 4cosy + 2x - sin2x = c O b. 4cosy + 2x + sin2x = c c.…

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Q: Show that the following equations are exact. Find solution. (a) dx dy_x– y³ + y² sin x 3xy² + 2y cos…

A: (a) The differential equation is given as dydx = x-y3+y2 sinx3xy2+2y cosx It can be rewritten as…

Q: solve the bernoulli equation dy/dx+y = y^2(sinx+cosx). and show that the answer is y(cosx+Ce^x)=1

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Q: Find / dy dx 174= √² y = √5 +1 and S=16x²= 2√

A: Note:-Since you asked multiple questions, according to our policy we can answer only first the…

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Check whether the given first order linear diff equation is homogenous or exact or separable or none…

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Q: Integrate fx cos(4x) dx fa

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Q: dx 1-S 1-sinx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: dy Q2) Solve x- 2y = x³ cotan 2x dx

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Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: Find dx * and then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t? –…

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Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

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Q: Determine the general solution: (dx/dt)A3 - (dx/dt)^2 - 4x = 0 Select the correct response: O y= c1…

A: Topic:- differential equations

Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: 11. y = (x + y) 12. y =x sin -1x + 1 – x2

A: Let's find.

Q: S. use "Exact Equation" method (cosxcosy + 2x)dx-(sinxsiny + 2y)dy = 0

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Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: y = eVx+cosx

A: To  findderivative of1)y=ex2+cosx

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: Find dx (e3t + 1)dt. -cos(3rx)

A: