4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: 3x sec (xy)dA; R={{x,y): 0 sxs7,0 sys 1}

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: t -1 b. y =: x² -x+2 à. y = c. y=3*hx t +1 d. y = (2x+1)°(3x–1) sin(xy) = x - y f. y=(In x)* е.

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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: y*dx-(ay + y° kty = 0 Let the substitution v=2; y=vx; dy=vdx+ xdv

A: Given differential equation is y2dx-(xy+y2)dy=0

Q: (xy² + 3y²)dy – 2x dx = 0 is not separable. ylgn ihi

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Q: 2. Obtain the particular solution A. yy' 2x(y+ 1) B. (x? + 1) dy = (y² + 1) dx

A: Topic :- Differential Equation

Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: x(x* +y° )°(vdx – xdy)+ y°dy = 0 Ans. (x² +y³)' = 6y° In

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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: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: Q6. If w = y²z² + xy and x = t³ – 1; y=t² + 2; z= 3t , find the total dw at t = 2 dt differential

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Q: 1D Y In y dr t t dy -d 2) x y(1+*)と'= 1+ y^ 3) (t+y)' Y'

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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: Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx…

A: Given that  The following differential equations

Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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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: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: (a) Find the differential dy of y = x² + 2x + 5. (b) Evaluate dy for x = 3, dx = 1/2. (а) dy 3 dx…

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Q: L{y'(t)} = sY(s) – y(0) y" + 2y" – y' – 2y = sin 3t, y(0)= 0, y'(0)=0, y"(0)= 1 L{v"(1)} = s³Y(s) –…

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

Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

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Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

Q: 5. Evaluateſ, x²y dx + xy² dy where C is given by: r(t) - 3t v(t) – et 0<t< 1

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Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: y1(t) 6y/(t) + 8y(t) = e2t + sin (t) ; y(0) = 0 ; yr(0) = 1 -

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Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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Q: (ztan 2 +1) dx – x dy = 0

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Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

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Q: (1, y' + 5y = f(t), y(0) =0, where f(t) = 0st<1 %3D t21

A: Solve the intial value problem using Laplace transferoms

Q: 1 calculate I f(x,y) dx and S f(x,y) dy 0. 0. 2 f(x,y) = 2xy – 3x %3D -

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Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: C:x=t4, y =t (-1<1< 1) 25. -ydx +x dy C : y² = 3x from (3, 3) to (0, 0)

A: First I have change the line integral into single variable using the given path and taking limit…

Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

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Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: •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

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: ii- (x* + y) dx - ry dy = 0, y(2) = 1 (using Integrating Factors)

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Q: 1(s* +r*)ds = s(s² -r*)dt =0 h. i. y'dy = x(xdy – ydx)e" j. r'y'= 4x +7.xy+2y²

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Q: Q3) Evaluate triple integral S" dz dy dx. x-y

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Q: t y + 4y + 3√ y(t)dt = 6-7 e²₁ y(0) = 1

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Q: dz 2) Find if z = xy² + x?y, y = ln x %3D dt

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Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.