7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

Q: 7/2012 - y x² + y² (²) di dx + (ye³ +2²) dy = 0

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Q: Find P.S. of (16x+5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-³)

A: The given equation is: (16x+5y)dx+(3x+y)dy=0⇒(16x+5y)dx=-(3x+y)dy⇒dydx=-16x+5y3x+y⇒dydx=-16+5yx3+yx

Q: 10. Evaluate: +4x dx (a) (b) (x2 -2x 4) dx (c) (t2-t) dt (et cos t) dt (d) dx

A: Here, we use the formula that integration of x^n is x^(n+1)/(n+1) as shown on board.

Q: If ( 1 + x²)(1 + y²) - px² = 0, where p is a constant, show that xy ( 1 + x²)dy/dx = ( 1 + y²).

A: Given: To Find:

Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: If w = (y-z)(z-x )(x-y),find the value of dw, dw, dw +- Z-X + dx dy dz

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Q: (у — ӕ + хусotx)dx + zdy — 0 y(0)= 3

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Q: II. Determine the solutions of the following DE. 1. xy'dx + (y + 1) e¯*dy = 0 2. (2xy – y)dx + (x² –…

A: note: as per our company guidelines we are supposed to answer only one question.kindly post other…

Q: dy 3. If y=u 3 and u = 4x2 - 2x + 5, give dx dy 4. If y=u? and u = x3 + 4 determine dx

A:

Q: If I = , 2x e*dx dy = then 1=

A: Given:     ∫11∫012xex2dxdy

Q: - (64 – 2²) " - dy dx %3D

A: Solve the initial-value problem for y as a function of x.     64-x2dydx=1 , y0=6

Q: (x² + xy – y²)dx + Gx? – 2xy) dy – 2xy)dy = 0 1 1 x3 +**y- xy? = C 1 x3 +x²y + xy² = C x²y Option 1…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if…

Q: 1. Evaluate ſ. (x² – y²)dx + x dy along c: x = t³, y = t 1st<8

A: Given:    x=t23 , y =t  (1≤t≤8)    =  ∫cx2-y2dx+xdy     =∫18t43-t223t-13dt+t23dt…

Q: Find P.S. of (16x +5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-3)

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

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Q: 25. (ye*" – 2y³) dx + (x e*' – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e* = 2xy³ + y² – 3.

A:

Q: Solve the following DE. 13. (5x + 3 e) dx + 2x e' dy = 0. 14. (3x + y-2) dx + (3x +y+4) dy = 0. 15.…

A: Given that: (5x+3ey)dx+2xeydy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: Which of the following is true if 2x y = 5 + "e* dt a. and y(1) = 5 e dx O b. dy 2eAx and y(0) = 5…

A: Explanation of the answer is as follows

Q: du _ dv dy dx If f(z) =z²+z - ,2

A: Take z= X+iY and proceed

Q: If y = u² + 6u - 2 and u = 4x² + 8x + 1. Find dy/dx.

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Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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Q: 7. If x + 3y'/3 = y, what is dy at the point (2, 8) ? dx 1 4 (A) = (B) 5 (C) - (D) 3 3 4 3/4

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Q: If y = 2u – 3(u² – 3u)* 3 (u² – 3u) and U = Vx –1. Find | | dy when x = dx 17

A: It is given that y=2u3-3u2-3u2 and u=x-1.

Q: If y=(6U2-7)3 and U=(9-2x)5 then find dy/dx and evaluate when x=5.

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Q: If ey 9 dy 3x and y(1) = 2, then the particular solution y(x) is %3D dx

A:

Q: What is the general solution to the following equation: (dx/dy)+ xtan(y)=2tan(y)

A: rewrite the given equation in the form of separable differential equation and integrate…

Q: If the substitution m = 2x - y was applied to the DE: (2x – y +1) dy + e2-dx = 0, the resulting DE…

A: Solved below

Q: Find the complete solution of the following. dy =  ( 2x3 + 4x ) dx         ;         x = 1 when y =…

A: From the given differential equation: dy=2x3+4xdx Now integrate on the both sides. ∫dy=∫2x3+4xdx So,…

Q: 5 To-4x D 5-2x NILS (6z²) dz dy dx

A: solution:-∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x6z3305-2x-y2dydx=∫0…

Q: 9. Obtain the general solution to the equation. (X² +36) dy + xy = 7x, y(0) = 2 dx

A: To obtain: The general solution to the equation X2+36dydX+Xy=7X, y0=2

Q: For the given DE: dy xy +y dx x2 – 5x + 6

A: Here we will find the value of y(x). We will gonna use a linear differential equation, L.D.E : dy/dx…

Q: 7. If S PCx) dx = 14 and %3D S.I find 6. fCx)dx

A:

Q: We have 3 3 27 dx dy = 4 y (x – 1)2 - Select one: True O False

A: Given query is to find statement is true or false.

Q: 24. Evalute dx r +1

A: Given: ∫0∞x12x3+1dx

Q: 4-compos dx dy 5-find dry if f(x, y) = xe xe 6- find (x²³/2)

A:

Q: 2 dy = Y – xy; y (–1) = 1 dx

A:

Q: If the substitution m = 2x - y was applied to the DE: (2x – y+1) dy + e2-dx = 0, the resulting DE…

A:

Q: Vĩ r3y p8- 8. dz dx dy 9. çdx dy dz хуг 2+3y² -3-3х с3—3х--у 7/6 c1 10. dz dy dx 11. y sin z dx dy…

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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: Obtain the general solution to the equation. dy 4. x+ 2y = x-3 dx

A:

Q: find general Solution of D.E. 4xydx +x'dy +3y^dx +2zydy=x

A: Note:- As per our guidelines, we'll answer the first  problem as exact one was not mentioned. Please…

Q: 11. Find if x? +у? %— ху. dy dx A. y'= x-2y 2x-y y+2x B. y'= Y x-2y C. y'= Y-2x 2y-x c y'= 2y+x x+2y…

A: The given function,  x2+y2=xy

Q: Find dz/dx if e² = ze®Y. ze*y. yz ey - xy ez – xy yze*y ez ery xzeyz et – etz - O yzet: etz – ez -

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Q: 27 dz, C: z(t) =t – ti, t e [-1,5].

A:

Q: 4. y(x³y³ + 2x² – y)dx + x³(xy³ – 2)dy = 0; when x = 1, y = 1 5. (2у — Зx)dx + xdy 3D 0 .3,,3

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Q: ve the given init value problem. dy dx 3x²y + y² 2x³ + 3xy' y(2) = -3

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Q: Evaluate ex+y dx dy In8 1-y y=0x=0 O e-In2 eln 8-7 025

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Q: y = 14. If u +4 u-4 and U= √x + x 10 dy , find dx when x=4.

A: This question can be solved using the concept of derivatives.