23. 3y(x? – 1) dx + (x³ + 8y – 3x) dy = 0; when x = 0, y = 1. ANS. xy(x? – 3) = 4(1 – y²)- |

Q: 1 5 X If y = - find dy dx at x = 2.

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Q: Compute dy and Ay for y =-4x – 3 at x = -1 with Ar = dx= -0.06. Give your answers to four decimal…

A: Given data: fx=y=-4x2-3, x=-1 and ∆x=dx=-0.06 We know that ∆y=fx+∆x-fx Substitute the values in…

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: 16 4+x² dy when y = Find 4 – x² dx dy dx

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Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: 19 271. dx y= 1-X) dy = -Ldx -dy= dx S-(-yei) y" dy 99 99 100 100 99 dy dy 100 %3D + R00 100 ). %3D…

A: Refer below

Q: what is the derrivative of y^3 + y^2cos(x) = x^3 -3x and what points in the function for dy/dx does…

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Q: 8. Find dy dx' x+2x given y = u³ + 4, u = .2

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Q: 2. Find the value of dx at y=2 if x=z²+5z and z= (y² + 2y)²/3.

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Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: 2. (1+Inx)dx +(1+Iny)dy = 0 when y( - 2) = - 1.

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Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

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

A: Given problems:-

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

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Q: Reducible to Exact (y3+2exy)dx+(ex+3y2)dy=0

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Q: 1. (2x – 3y) dx + (2y – 3x) dy = 0 - -

A: According to our guidelines we can answer only three subparts of a question, or first question and…

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: у (9х — 2у) dx - x (6x = y) dy = 0 -

A: Given:- y (9x - 2y) dx − x (6x — y) dy = 0 To find:- Solve given differential equation when x=1, y=1

Q: 4. (x +y- 4) dx - ( 3x-y-4) dy = o when x=4, y=!

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Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

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Q: 2. Find an expression for dy/dx on the curve x In(y) + x³ – 2y = 6.

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Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: y= In]3x+2)²/2x–1 dy 1. Find dx

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Q: Cln S iny 7. ex+y dx dy 0.

A: I=∫1ln8∫0lnyex+ydxdy⇒I        =∫1ln8ey∫0lnyexdxdy               =∫1ln8eyex0lnydy…

Q: dy In(5x + 5) Find for y = - dx 3e2x dy dx

A: Given, y=ln(5x+5)3e2x

Q: 9. If dy = xy² and if y = 1 when x = 0, then when y = 3, x is equal to dx 0 -0 DIE

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Q: 17 (7+ x²^ dy when y = dx Find %3| 7 – x²

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Q: find dy/dx: (x+y)3+ (x-y)3=x4+y4 ?

A: The given equation is x+y3+x-y3=x4+y4. Find the derivative dydx using implicit differentiation as…

Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: 4. if x^3+y^3=2 find the value of (d^2y)/(dx^2) at the point (1,1)

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Q: 3. Find dy/dx of: x(x-y)-xーy evaluated at x = 0.001 and y = 0.002

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Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: dy 4. if y = csch-1 2º . de 2x+2 dx . 5. J2-2x+1 x² –2x+1 dy 6. dx if y = (1+ x²)etan-1x

A: Given; 4. y = csch-12theta 5. Integration of the term (2x+2)/(x2-2x+1) 6. y = (1+x2)etan^(-1)(x)

Q: 1. Non-Exact DE (4x² – 4xy + 3y² + 2x – 3y)dx +x(2x – 2y + 1)dy = 0 -

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: 3 -V7 dz dy dx dy dz dx

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Q: 1- [(2x – 5)/3x – 1) dx | 2- S S(x3 – 10 + 3y² dy dx

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Q: dy 3 (49-y²) 2

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Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

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Q: 3. Find dy/dx of: x'(x-y) -x-y evaluated at x = 0.001 and y = 0.002

A: The given equation is x2x-y2=x-y2 at x=0.001 and y=0.002.

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

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Q: (1+ 4ху — 4x?у)dx + (x? — х3 )dy 0; when x 2, у %3D - -

A: Definition used -               Variable separable differential equation-               A…

Q: 4. (6xy³ + 2y*)dx + (9x?y² + 8xy³)dy = 0 5. (у2 — 2ху + 6х) dх — (x? — 2ху + 2) dy — 0 When: x =…

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Q: If y = (4x² – 3x+ 2)(e2* – cos 3x), then find dy at x = 0. dx -2x %3D - -

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