What is the general solution of the following ODE* 3 points (x² + xy – y*)dx + (;x² – 2xy) dy = 0

Q: 2 A manufacturer makes a product, of which the principal ingredient is a chemical, X. moment, the…

A: From the given data, State of nature Course of action    S1 (Use Y and Z) S2 (Use X)…

Q: Evaluate the integral. 3 1 3y2 cos xy dy dx x/3 5(1 - cos 3) 3(1 - cos 3) cos 3 - 1 (1 - cos 3)

A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

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Q: If y- In(3 sinh( 3lnx)), then xy'= Select one: O3 coth( 3 Inx) O 3 /sinh( 3 Inx) O 9 coth( 3 Inx) O…

A: Use the Chain-Rule of differentiation to differentiate the function y.

Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: What is the particular eq. of the given: y"+9y=e^x (cos 3x)+ x² + x³ex

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Q: 1) y = 2sin (5x) ,2) y = In x'n cosh 5x ,3) xsin=14y = y tan-14x 4) y = ecosh (8x),5) y =- t +1 t…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

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Q: If xy In(3 sinh( 3x)), then x2y'= %3D Select one: Ox coth( 3x ) - In( 3 sinh(3x)) 09x coth( 3x ) - 3…

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Q: Construct an example of an non-homogeneous ODE that cannot be solved using method of undetermined…

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Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: 2 In cosy y4 1 [1] limy-0

A: After simplifying the function the form is 0 by 0. So, apply L'Hopital's rule to find the limit.

Q: 19. Evaluate: S A. VT- x² + arcsin x + C C. – VT- x² + 3arc cos x + C B. – VI- x2 +3 arcsin x + C D.…

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: Which of the following is true? O Scos(3x)cos(4x)dx= [ r cos(x) + cos(7x) dx B Jsin(3x)cos(4x)dx= […

A: Option D

Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: Find * In(x² + 2x + 2) dx (x + 1)² In|1 + (x + 1)²| x +1 In|1 + (x + 1)2| x + 1 + 2tan-(x + 1) +c…

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

Q: Evaluate the integral. (sin Sx cos 5x dx 늘 cos 13x-5 cos 3x + C 26 1 cos 13x - 26 1 sin 13 x + C 26

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Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: 1. Evaluate 5 S Sx (x + 3x)dydx

A: Given, ∫05∫0x x(x + 3x) dy dx=  ∫05∫0x (x2 + 3x2) dy dx=  ∫05 ∫0x (x2 + 3x2) dydx= ∫05 ∫0x 4x2 dydx

Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

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Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: If y = (3x²+5) (2x³ - 5x – 4) then dy/dx O (3x2+5) (6x² - 5) + 6x (2x3 - 5x - 4) O (3x2+5) (6x² - 5)…

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Q: y" +y' = cos 3x

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Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

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Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: The integral of the given function csc °x dx is equal to 3cos x-10stn²x cos>x-15sin"xcosx + C…

A: I=∫ csc6x dx =∫ (cot2x+1)2 csc2x dxu=cot xdu=-csc2x dx=∫ -(u2+1)2 du      =∫(-u4-2u2-1) du…

Q: Suppose that the position of one particle at time t is given by X1 = 5 sin(t), Y1 = 2 cos(t), osts…

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Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 8 8 + 4 sin(3x)cos(3x), sin(2x) +…

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Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: 1 Evaluate | (x²sin y- xcos(y))dy O 2sin y-3cosy + C 6 -3sin y+2cosy +C 6 x2(1- cos(1)) – xsin(1) +…

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Q: 11 Show that Simpson's rule withn=2 (so there are 2n = 4 subintervals) gives the exact value of (2x…

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: 17. Evaluate f-3x cos 2x dx a. --cos 2x - 3xsin 2x + C b. -cos 2x -sin 2x + C C. -cos 2x -³x sin 3x…

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Q: 1. If y = cos(2t + 5) find using chain rule dt

A: Giveny=cos(2t+5)

Q: 6. x sec x tan x dx

A: Let's find.

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: 3 – 2ry' + 2y = x° sin x

A: The general solution will be the sum of the complementary solution and particular solution.   The…

Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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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.