S o l v e    t h e   e q u a t i o n s .  (2x − y)dx + (4x + y − 6)dy = 0

Q: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…

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Q: Show that if y(t) = x(t) * h(t), then y'(t) = x'(t) * h(t) = x(t) * h'(f) %3D Show that x(t) * 8'(f)…

A: We only solve one problem at a time So please submit them one by one.

Q: D. f(x, y, z) = 1x + 10y + 8z Vf(x,y) =i+j+k E. f(x, y, z) = 1x² +10y² + 8₂² ▼ f(x, y, z) =i+j+k

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Q: Choose the letter of the correct answer and justify or defend your answers. |Identify the 3rd order…

A: Given that: Differential equations as shown

Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 5x, x = 4, Ax = 0.5 Ay = Ду %3D dy…

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Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: E q u a t i o n s     o f     O r d e r     O n e   :  S u b s  t i t u t i o n  Suggested by the…

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Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

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Q: (xy - y) dr - x'dy = 0 %3D O x = c e Dy = ce I x = c In Oy = c In

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Q: (xy + xz + yz) dV; D= {(x,y,z): - 1sxs1, -3sys3, - 2szs2} D Se (xy + xz + yz) dV = (Simplify your…

A: Consider the given expression as ∫∫∫xy+xz+yzdV

Q: ( b) SI[ vzcos(x* µV where E = {(x, y, z) |0 < x < 1, 0 s y s.x, x S z 5 2x } E

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Q: F i n d   t  h e   g e n e r a l   s o l u t i o n .  (2rm − 3r2)dr + (r2 + m)dm = 0

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Q: F(s - a) "Y(s) – s"-ly(0) -...- y(n-1)(0) L{f *g} F(8) G(s) -as L{U (t – a)} L{f(t - a)U (t – a)}…

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Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: (y² + xy³)dx + (5y² – xy+ y³ sin y) dy = 0 Let M = y² + xy³ and N = 5y² – xy + y³ sin y 1 /дм 12. M\…

A: Given M(x,y)=y2+xy3  and N(x,y)=5y2-xy+y3siny

Q: L{y'(t)} = sY(s) – y(0) y" – 4y' = 6e" – 3e', y(0) = 1, y'(0) = -1 L{v"(t}} = s°Y(s) – s y(0)–y'(0)

A: NOTE: Refresh your page if you can't see any equations. . take Laplace

Q: Construct the Green's function for d²y dx² dy + (k?x² – 1)y = 0, + x dx subject to the boundary…

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Q: z = In (VT" + y") If With n e N, n > 2, Then the result of 2 (dz dy dz n Corresponds to: "-1 + y"-1…

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Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 if M - N? = 24M, M,N, = 1 and M? = 2 - N? then an…

A: We have the differential equation Mx,ydx+Nx,ydy=0 If Nx-MyM=fy then the integrating factor is…

Q: /// 2xz dV where = {(x, y, z) | 1 < x < 4, x < y < 2æ, 0 < z < x + 3y} Evaluate E E %3D

A: We are asked to evaluate the integral.

Q: ƏN 10. =? (a) y (b) —у (c) 5y² + y³ sin y (d) 5y² – y+ y³ sin y

A: Topic = Derivative

Q: C o n s i  d e r      t h e         p  a r a b o l a   C   :   z   −   4   =   − ( x   −   2 ) 2   o…

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Q: e^x + y)dx +(2 + X + ye^y)dy= 0 ,y(0)=1

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Q: e 2x1nx 3. a) Differentiate w.r.t x y = (x-1)3 dy b) Determine dx given that x = te-t and y = 2t2 –…

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Q: a. (x² + y?)dx + 2xydy = 0 a2u b. ax2 a?u a?u с. уу"" — х dzy d2x d. x + y dt2 = C1 dt2 e. y"+ 2y' –…

A: Given. Given are five different type of linear differential equation and we need to categorise them…

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 6x, x = 5, Ax = 0.5 Ay = dy =

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Q: For "IVP" (dx/dt)+2x=uπ(t)sin(t) ; x(0)=0, if we apply Laplace on the equation, then (S+2)(S2+1)x=?

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Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: S o l v e   t h e   e x a c t   d i f f e r e n t i a l  equation (v + t)dv + (v - t)dt = 0. a. v2…

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Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 – 5x, x = 4, Ax = 0.5 Ay = dy %3D

A: Given data:   The given expression is y=x2-5x. Th given value of x is x=4. The given value of change…

Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: a:) x*y" + xy" • e" b.) (xty) de + (3x² -1) dy =0 c.) x² dy de? dx 2 t xy = sin (x) d.) c) (x²ty*)…

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Q: Use the graph to match the integral for the volume with the axis of rotation.

A: Let's check each options. When axis of rotation is x - axis, then strip is vertical So inner radius…

Q: dy = f(x, y) = x' + y', y(1) = 5 %3D dx 39- find y(3) value by euler method, take step size; h= 1.…

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Q: H.W4 1: find of/ox and of/oy.. a) f(x, y) = Vx² + y? e f(x, y) = e* sin (x + y) %3D b) F(x, v) =…

A: Since you have not mentioned any specific question number i do the highlighted question (b)

Q: dy + 4y = 8 dy d. x- dx = (x – y)² %3D a. dr dy e. da dy + 4y = x? %3D b. = V1+x2 %3D dx dy dy c. dr…

A: This can be solved as follows:

Q: Which of the following first order is linear? (¹) ¹/x = ¹ ex (六) a dx x A. B. (1) dy dx = 1 ex c.…

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Q: 5. y' + 2y = 0, when x = 0, y = 2 %3D Ans. y = 2 e-2x %3D dy 6. xy +2 y– x - 2 ху — Зу+х-3 dx (у -…

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Q: Given: xe + In(x - y) = . Find dy/dx. %3D O dy 2ry(x-y)e+x+a*(z-y)(2a+1) da r +z? (x+y)e? 2a…

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Q: : // (x + y – 32) dV where E = {(x, y, z) | 0 < y < 1, 0 < x < y, 0 < z < r + y³} Evaluate - E

A: Triple integration

Q: dt (b) z = x?y where x = st and y = t2 – s2 dz 2st?(t? – s?)? – 4s³t²(t? – s²) as answer: az 2s²t(t?…

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Q: If (xy + ny?+ x + 1) dx + (y + am) dy = 0 is separable, then (A) n = 0, m = 0 (B) n = 0, m = 1 %3D…

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Q: Find the particular solution of the differ ential equation xy(y² + 1)dx + (x²y² – 2)dy = 0 when x =…

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Q: Consider theD. E. M(x, y)dx + N(x, v)dy = 0 if M – N = 24M, M,N, = 1 and M = 2 - N? then an…

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Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: F i n d   t h e   g e n e r a l   s o l u t i o n . (2x – 3y + 2)dx + (2x – 3y + 1)dy = 0

A: We will use a substitution to solve the equation.