•ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

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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…

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Q: find ƒx , ƒy  . 1. ƒ(x, y) = ln (x + y) 2. ƒ(x, y) = sin^2 (x - 3y)

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Q: Solve the homogeneous DE. 3. (x – y sec?2 – x tan2) dx + x sec² 2 dy = 0 -

A: Given that: x-ysec2yx-xtanyxdx+xsec2yxdy=0

Q: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: Solve (y cos x – 3x²y – 2x)dx + (2y sin x – x° + In y)dy = 0 Solve x sec (ry)dy = -[y sec (xy)…

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

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Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

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Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: y" + y = tan x; y=-(cos x)ln(sec x + tan x) d²y 42 + 4y = 0; y = cje2r + czxe²* dy dx dx + 2x² d?y…

A: Given : (1) y'' +y = tanx (2) y'' -4y' +4y=0 (3) x3y''' +2x2y'' -xy' +y =12x2

Q: 4 I. dx3, (d³y\ dy + 2- dx = sin x *+ O) + = In y. 3 II. dx dx dx d³y III. dx3 d²y , dy -2 + dx2 = x…

A: To identify which of the given differential equation is linear.

Q: (4,0,2) S sin y cos x dx + cos y sin x dy + 3 dz (1,0,0)

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Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: 8/ (e* sin y +3y)dx -(3x-e* sin y)dy = 0

A: Given thta  The differential equation

Q: -2x + 3x -x) dr- (sin y + y e (y e + +3y e) dy 0. x(0) 1 D 2r-- O 2y - y+ xr e O x+ 2x-y e-3y e+3e–…

A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: O1 Find: fx³ cos x dx using Integration by parts b. ſ cosx? 2x dx using Substitution Method a.

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Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: x+1 ²+1 sin(x² + y²) dy da equals sin(x² + y²) dx dy y-1 O ² sin(2² + y²) dz dy

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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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. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +…

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Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: find ƒx , ƒy  . 1.ƒ(x, y) = e^(xy) ln y 2. ƒ(x, y) = cos^2 (3x - y2 )

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question…

Q: hW (3 Xy'a4Y) dx + (3 X*y'+2x) dy = o I) sin X dy - Sin 2X -y Cos X dx

A: Given

Q: 1. S(tan -1)ʻ dp 2. sin2 B cos B dB .5 xdx 3. S (-7-8x-x* 4. Sx³ (a2 + x2) dx xdx 5. f (x²+a²)³ 6.…

A: (2)

Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: 3. у(3x3 — х + у)dx + x?(1 — х?)dy 3D 0 4. у(2х — у + 1)dx + x(3х — 4у + 3)dy 3D 0 5. (r + sin 0 –…

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Q: 2) (2x + sin x) dx + x cos y dy = 0 3) - 2y + a = 0 dx dy 3y 4) r2 (Exact). (Separation variables).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 1. 2sin?2t dx = cos x(1 + cos 2x)dt 2.3e-3y dx – ee+xx-2dy = 0 3.x*ydy — ху?dx + 3ydy - 2xdx %3D 0

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Q: 3 sin y 2. Find the particular solution of xsin² y cos yy' +. 1+ ln x =4 ¡y(e) = 1/

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Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

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Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

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Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: 2. (sin y)[x+sin y]dx+2x cos ydy = 0 sin y 3 Ans. x = C sin +3x y

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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: 1. dy = 2 – y²dx 2. x(1+x* )dy =(y +y x²-x* )dx 3. ( y² – 1) dx + (2xy – siny)dy=0 V2x-x2

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Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

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Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

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Q: me general solution of (D²-2D+1)y=2sin > A y=c1eX +C,xe* + sinx+cos x y=C1eX +C,Xe* + sinx ©…

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Q: Find dy/dx. y = x' sec (-). A 1 sin 3x cos + x sin2 5x (e) B) x sec 5x sec C) x sec sec D x sin 5x…

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Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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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…

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.