| (h(y) – 4)dy = 18 h(y) 9(y) 1 |dy 19 12 15 18 - 18 - 7g(y)dy = 1

Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A: Given ∫23∫-14∫104x2yz-z44dz dy dx ∫23∫-14∫104x2yz-z44dz dy dx=∫23∫-14∫104x2yz dz dy dx -…

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: 3. II Azy'dz dy = 2y°(3² – 1)dy | 2y (y? – 1)dy 1

A: Given that a double integration .We use general  property of integration to solve this integration.…

Q: /1- (z² + y²) dz dy dæ ) Evaluate

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Q: 6. (6x – 3y + 2) dx - ( 2x - y– 1) dy = 0 ans. 3x - y + C = 5 In | 2x - y + 4|

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Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: 2 dx + ( 2x-y+3) dy = 0 ans. y + C = - In |2y-y+4|

A: See the details solution in below

Q: 8. Jydx + (1+ x)dy = 0,,when x = 1, y = 4

A: Differentiable equation can be solved separating the variables on each side and then integrating…

Q: 1 [ (2 -y - VE) dy 2 – y – 0. 1 | (2-y (2 – y – V9) dy 0, 2 | (x² – (2 – æ)) dæ - 2 [ (2² – (2 – a))…

A:

Q: dy/dt^2 – 4dy/dt – 5y =0, y(1) =0 ; y’(1) =2

A: Given differential equation d2ydt2-4dydt-5y=0  , y(1)=0 and y'(1)=2

Q: 26. Evaluate (x³ + y² + z)dx dydz.

A:

Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: 10) *- dy + 8, y(1) = 1 10) dx A) y = Vx + 8x - 8 В) у%3D 1 + 8x - 8 27 C) y =x + 8x + 10 D) y = +…

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Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

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Q: dy 5. S: y(1-Vy)2

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Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

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Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: 3y 6. S dy y-3 7. SVIV7+xVx dx 8. S dr V1+r3

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Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: [2x*yžcosx² – 2x*yå + x/5]dx + [x/5stnx² - x° /9]dy = 0 3 2x²yz + x [x/ysinx? – x³ /y]dy = 0 -

A:

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: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

A:

Q: dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

A: Given that, dxdt=x-y+tdydt=x+3y+t+1 This can be written by, X'=1-113X+tt+1 Now the homogenous eigen…

Q: 2. [e2y ycos (xy)| dx + 2xe2y [2we?y xcos (xy) + 2y dy = 0 -

A: The solution is given as

Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

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Q: 2 4. S dy 1 y +y° - 3

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Q: d?y 4- dt2 dy dy (-2) 9. + 28 + 49y = 0; ; y(-2) = 2 ; = dt dt 2 d?t dt + 9 dx dt (0) t(0) = 3; dx…

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Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

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Q: + 4 oly +6y =0 dt dy +2 -6x=6

A: Introduction:Simultaneous equations are those in which the derivatives of two or more dependent…

Q: d*y 4)5t- dt + 3t () – (sin t)y = 0 dt 4 5)(sin x)y² + 2 y = 3x³ – 5 %3D 6) xy ? + 3 xy - 2 x³ y = 7

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Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

A:

Q: 2. a*y(4) „4„(4) + 6x°y" + 9x²y" + 3xy' + y = 0. 3. (x – 1)2 d²y dx2 - 2(x – 1) dy + y = x + 4. dx -…

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Q: d²y 5 dy +6y= e7t dt dt2 y (0)=0 y'(0)=2

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Q: - If y = u – 4u and u = = 3x + r, then dy с. dr 1 dy а. dx 12x3 + 1 12x3 + 1 3u? 4 dy (3u² – 4)(12r³…

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Q: 2y4 y3 – y2 + y – 1 dy = y² + 2y + In ly – 1| -in ly2 + 1| - y +C

A:

Q: d'y dy dy -+6 +11-+6y=4 dr dr dt y(0)= y'(0)= y'(0)= 0

A: Given the Ordinary differential equation:

Q: 3- dy + 3x^²y = x³6 s dx Y- XLnx dy dy +y = ₂l₁x dx 2Lnx ets

A:

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: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

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Q: 1 dz -÷z³ = t² + 3t – 2 dt 3 z2 -

A: Differential equations and their type

Polynomials

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