(g) y dx = (y + xy²) dy separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y Onone of the above dy (h) X = yexy - x dx O separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the above (1) xyy' + y² = 2x Oseparable exact linear in x O linear in y O homogeneous Bernoulli in x Bernoulli in y Onone of the above

Q: y'(y-1)d(x-y)-(x- y)dy' y2(x- y)² +(1– y')² y'(x- y) arctan tan - 1- y

A: Use the following formulae, to evaluate the given integral.…

Q: of and for the functions: dx dy H.W: Find 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2) 2. f(x, y)…

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Q: Let [² f(x) dx = 2, f'se Find (* 160). f(x) dx = and 1 [₁² [F(x) dx = 5, Fox) dx = 4 f(x) 0 2f(x) -…

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Q: + ( Xyz

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Q: x³ y" + xy' - y = 0 [ Hint: x = e¹, ln x = t; x(dy/dx) = dy/dt; x²(d²y/dx²) x³(d³y/dx³) = (d²y/dt2)…

A: The given differential equation, x3y'''+xy'-y=0 We have to find the general solution of the…

Q: 5 find dy/dx for y= [(r^2+1)] ^(-1) ,x= [(4r+1)] ^(1/2) (use chain rule) 5-find for y= (r² + 1)~1 „x…

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Q: Differentiate y = sin(3x + 4y) cos(3x+4y) 1+ 4 cos(3x+4y) з cos(3x+4y) 1+4 cos(3x+4y) cos(3x+4y) a.…

A: y=sin3x+4y

Q: In (In y) xy³ dx + x²y2 dy + In x dy = 0 dx + %3D y In y

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Q: ах ) x' + 4x/y 5 y² = 3 ) Vxy +1 = y ) 3xy = (x' + y' ) ) x' +x.tan¯' y = y ) sin¯'(xy) = cos"' (x –…

A: Simple differentiation

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

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: -n If y=a(x+ Vx* +1) +b(x - -1)" prove that .2 (x²–1) d'y dy n°y =0. dx dx

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Q: +4x 6) y' = Ans.: y-x =e +C. 3y - 2xye"

A: According to the guidelines in case of multiple questions we are only allowed to do first question,…

Q: 2y (1) (x²+2x) dx = (3 - In x²) dy separable exact linear in x linear in y homogeneous Bernoulli in…

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Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

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Q: is D.E xy? dx + (x+y) dy= 0 a- linear b- Exact C- non_linear ( Explain that)

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Q: linear or not linear? 1) dy 1ax +exy = x²4² dx 2) y + e* sinx= x³y² 31 y\nx - x²y = xy! 4) dy + cosy…

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Q: y dr -| 3x (y- 1) + 2] dy = 0 O xy' =c e" - iy - y - O xy' =ce"-y + ty- O x'y = e-iy- y-+e n xy =…

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Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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Q: 5-find for y= (r² + 1)1 ,x (4r + 1)2 (use chain nule) %3D dx A)y Vr+1 (r2+1) dx dy r(4r + 1) B) dx…

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Q: dy Find dx at the point ( x, y ) = (1 , 0) If e *y = e * In(x²) + y² + 1 %3D

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Q: (x+y )dx+(x-xy)dy 0

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Q: (x + 2) y' = xy + 23-3x-6, when x 0, y 1 O y = 2-e O y = 3- 2e* O y = 1+2e* O y = 3+ 2e * %3D

A: Solution of differential equations

Q: If (2xy?+4) dx +2 (x*y-3) dy = 0 then ƏP/ay # ƏQ/ax *

A: Given: The equation is, 2xy2+4dx+2x2y-3dy=0 And ∂P∂y≠∂Q∂x To find: Whether it is true or false.…

Q: ay + 2y = 3 dx %3D dy + 4y = x³ - x dx dy .2

A: A first order linear differential equation is expressed by the form  dydx+Py=Q Here, P and Q are…

Q: (1 + Iny-) (;++i" y) dy = 0; 7. dx + y(2) = 1 Ans: In y+x+xIny-=0

A: The given differential equation is  1+lny-xy dx + xy+x22y2+3yln2y dy =0   ;  y(2) =1 Compare with…

Q: SHOW WHETHER THE FOLLOWING DE IS EXACT OR NOT 1. (y^2 – 2x)dx + (2xy + 1)dy = 0 2. x[1 – sin(y)]dy =…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Find the line integrals of F = 2yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: Suppose that f(x) .is an invertible, differentiable function for all x and the following facts are…

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Q: xt' + (t")3 = Và +5 x (3y')² ex² - y² = = (4x²y³ + y)²¹ y" 4 (cos x)² - y"

A: The given  differenrtial equation is xt'+t''3=x+54 Calculate the order of given differential…

Q: (i) / x(V - 4) da. (H) / z*e* 1. Find „4p-3r³+7 3 – x2, 0<x <1 0 <x < 1 2. Evaluate | f(x) dx, where…

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Q: Find a solution of x = y²_ (a) (0, 1) 1 1-xec y = (b) y = dy dx (0, 0) y = (c) (-1/2-1/2) (d) (2,…

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Q: ди ди + 2х. -00 1, t- 1, a + 2x- dt dx и(х, 1) %3D f(x).

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Q: (dy = arctan dx, (i) Use the facts: dy and (dy/dt) to find dt d dx (dx/dt) ds (ii) Use the fact that…

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Q: 3.) dy_x²(1-y) = 0 dx

A: To solve the following 1st Order Linear DE.dydx-x21-y=0

Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…