ysin2-xcos2x dy = 0 16. x cos + ysin2} y sin r cos Ans. xy cos y = a dx dy y+Vx +y? 17. Ans. y+Vx +y? = Cx² %3D

Q: 7- cos y dx + (x siny - cos²y)dy = 0

A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: 3(sin y- cos y)* dy cos y

A: We need to solve the integral ∫3sin y-cos y2cos ydy Now, we have an identity a-b2=a2+b2-2ab Hence,…

Q: 1. (xy + x)dx + (x³y² + x² + y² + 1)dy=0 (Separation of variable) 2. (y? cos x – sin x)dx + (2y sin…

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Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: Given: a = 0 – sin 0; y= 1- cos 0 d'y Find: dz2 O d'y 1 dz2 (1-cos 0) d'y 1 %3D dz2 (1-cos 0) O dy 1…

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Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: 2. 2x?cos y dy + sin y ( x+ siny)dx

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Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: 7 Find dy (b) x siny-ycosx-y = 1. dx

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Q: 4) S(x, y) = (4x-x* )cos(y) on the Ans. Absolute max.: 4 at(2,0) 3/2 Absolute min.: at 2 rectangular…

A: Given

Q: Ho Find (dy/dx) for: tanh-¹(x y) + e(x+y) 5 cos(y)

A: It is given that, tanh-1xy+ex+y=5cosy. The objective is to find dydx. Formulas used:…

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

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Q: Double integral of x^3 cos(x^2y) dxdy ? for x=1/y, x=1/2 & 1<y<2

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Q: dy x COSY dx - siny=0 6 xcos)

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Q: x cos'(y)dx + tan y dy = 0, y(4) = 7 2. X COS

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Q: Find dy/dx by implic differatiation. a) x^3-xy^2+y^3=1

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

Q: 3. dy - 2** + e 2x cos (x) + Cos(x) y Fuctor8 Integrating

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Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x3 + Iny) dy = 0, when x = 0, y = e

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

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: dy Find for y = - 19x+3 cos x. dx dy

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Q: 5. (1- xy)-dx + [y2 + x(1-xy)-]dy = 0 6. (y- cos?x)dx + cos x dy = 0

A: Exact differential equation. An ordinary differential equation Mx,ydx+Nx,ydy=0 is said to be an…

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: dy Solve for dx sin y+ysin x given xsin y- y cos x = 5 А. cOS x+x cos y sin y-ysin x B. COS x+x Cos…

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Q: 2/ Find dy To y=sin h'(tanx) 2-y (X+1)}

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Q: dy x(2 In x+1) 1. dx siny+y cos y

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: ( cos x - 3xy- 2x) dx + (2y sin x – x+ In y) dy = 0, y(0) = e

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Q: 7. (a) Find dy/dx, when x = a(1 + cos 0), y = a (0 + sin 0). (b) Differentiate xcosx w. r. t.…

A: Differentiation using Logarithms: When a function appears as an exponent of another function we make…

Q: dy Find at x=0: dx y = (In(cos "x*) -1 COS sinh x %3D

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Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

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Q: 1. (2xy-tany)dx + (x² – xsec?y)dy = 0; y(1) = r 2. [4x°cos(xy)-x*ysin(xy)- ye" +3x²]dx…

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Q: 5 (2xy* + sin y) dx + (4x²y³ + x cos s y) dy = 0 %3D

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Q: z=cos y Using the substitutions the DE (3cos y – 5x)dx – 2x?tan y dy =0 reduces to dz = - sin y dy A…

A: Using given substitution.

Q: (ye*y)dx + (xe*y + sin(y))dy = 0, y(0) = t exy + cosy – 1 = 0 ЗехУ — сosy — 2 %3D 0 Option 1 Option…

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Q: 7- cosy dr+(x siny-cos y)dy=0 8- (1+y)dx+(2xy+ y +1)dy = 0

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 9. (siny - ysinxy)dx + (xcosy-xsinxy)dy 0

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

Q: 3. sin y(x+sin y)dx + 2x² cos ydy = 0 0: uhen v-2

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Q: 1) S 2 sec y (tany – sec y) dy

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

Q: 25. (2y cosx + sint x)dx sin x dy , when x =y = 1 %3D %3D

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Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

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Q: 1. Find given x = 0 - sin 0 dy dx' y = 1- cos 0 1. Find dy given x = et-cos t y = et - sint 3. Find…

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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.