16. If (2i + 2j) x (i +j-k) =-di + 2j - k then A A A -3 B -2 C 2 245 D 3

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: 21. Кх, у) 2х -у ys 4x + 6 5 * 4y s 7 2r + ys7 бу X-6y z 10

A: Step-1 f(x,y) = 2x-y            y ≤ 4x+6 ⇒ 4x-y ≥-6            x+4y ≤ 7           2x+y ≤ 7…

Q: 1- If y+3y = 8 then g-solution is %3D a- y+ 6 = 1 In (8-3y) = x +c a.

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Q: (4) Suppose that z = xy², then =( (A) xy2 (B) 0 (C) y² (D) 2xy (5) Suppose that 4-{(rw) 6 ²2 2 ).…

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Q: Solve: ()* +1 y In z 6x In a+ 2x = 9y + 36y + 18 In y + C O 6x* In z – 2x = 9y? + 36y + 18 In y+ C O…

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Q: 25n Evaluating sec will yield to 6 V3 A 2 2/3 B 3/3 © - 2 V3 D 2.

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Q: 8. What is the particular solution of 2xyy' =1+ y², when x = 2, y = 3 ? C. y =V5x +2 d. y =3x – 4 a.…

A: Given differential equation 2xyy'=1+y2, when x=2,y=3. The objective is to find the particular…

Q: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: 4[8,(t-2) rect(r)dt

A: we have,  I=4∫020δ4t-2recttdt we know that  ∫t1t2xtδt-t0dt=xt0 ;   t1<t0<t20       ;…

Q: 1. Find x, y, and z so that x + y 4x 2y -16 -- y 11 4 Z

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Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: 2 3 Compute fyz, if fx, y,2) = x² -x³y² -z'. %3D xyz» OA7 B. 5 OC.0 D. No one correct. O E. 6

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Q: What is the particular solution for y′=6e^x+x^2−7x such that y(0)=6?

A: Given problem:- y'= 6ex+x2-7x  Particular solution for given differential equation when y(0) =6

Q: 8.) if z = x +jy, then Rez + Imz= (2+2) + ½/₂ (2-2²)

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Q: 3 If z= then: (2x² + y² )² ' dz az + y- -4z he dz dz + y- 4% az dz + x- y- = 4z az az = -4z

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Q: 5. Given that mz1 42°, mz2 = x2, mzC =D %3D K C E D

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Q: If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8 -3y ) = x + c %3D

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Q: 3. Show that y = 5x2 +2 is a solution to the DE ry' +y" = 2y.

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Q: 10. Find the particular solution that satisfies the initial condition. my'+2y = 3x2-5x, Initial…

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Q: 4. Solve eu, - uu, = 0, u(0, y) = -y %3D for small |r.

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Q: 4. Find the number of non negative solutions to x + y + z = 21. With the conditions that x > 3, y >…

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Q: Solve (» — 1) dz — (За — 2у — 5)dy — 0 - (2у — х — 3) — C(у — х+ 2)? О (2у — а + 3)? — С (у — х + 2)…

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Q: 9. If x2-xy + y2 = 3, find y' and y", %3D

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Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: 2. (1 + x²)y" + 10xy' + 20y = 0 (-1)*(2k + 1)(2k + 3)(k + 1)a,x²k - (-1)*(k + 1)(k + 2)(2k +…

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Q: 1 10. Evaluate dydx, where X> 0. A) B) C) D) 4ª E) 4X7

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Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: 18. If x² + 2xy = y² then y' is b. 2x + 2y d. -x

A: (18). Given: x2+2xy=y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law:…

Q: If A= and D = A+B and d2--1.d, 2 then 1. x=-1.y = -1 2. x=-1.y = 1 3. x=-2 y =1 4. x-2. y --1

A: We have to find the required values of x and y .

Q: 3.11. dz, a) y:|z + 2| = 1; (z -1- 3i)(z + 2) 6) 7:|z +1- 2i| = 3;

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: 2- Show that: 2 J1(x) = (-1)m x2m+ (2m + 1)! m=0

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Q: 6y" – 7y' – 5y = 2x³ + e¯* – 5 -

A: Ordinary differential equation involves the derivative of single dependent and single independent…

Q: 10. Particular solution of y" – 64y = 16, when x = 0, y = 1, y' = 0 %3D

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Q: 1. (1+ V)²dx 2 2. (교2-z) dr (r-1 +x)2 3. xp-

A: solve the following

Q: 4. The line 3x + 2y – 10 = 0 is perpendicular to Ax + By + 1 = 0. Find the possible values of A and…

A: Consider the set of simultaneous equations, 3x+2y-10=0………(1)Ax+By+1=0…………(2) Let m1 be the slope of…

Q: 1. y = x - 3x2 + 3x + 2 fonksiyonunun ,-2,2| aralığındaki en büyük ve en küçük değerini , yerel…

A: If 1st and second derivatives of a function at a point is 0, then that point is inflection point.…

Q: dx = Select one: a. In|x-2|- Inlx +2| +c b. 글미x-21- imx + 리1 + c C. 글미-2-글 i미x+ 21 + c O d. In|x-2|-…

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Q: (,² + 4y² )0.5_x = se!y =r!0in(r) find Ou 2 0.5 when s= 2, r = 4,t = -3

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Q: Evaluate the integrals

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Q: a) Evaluate ²₁ √√1-x² √√1-x²-y²e-3(x²+y²+z²)² dz dydx

A: The given problem is to evaluate the given triple integral of Cartesian coordinates.

Q: What is the particular solution of 2xyy' = 1+y2 , when x =2, y = 3

A: The given differential equation is solved below in detail.

Q: 5 10-2z 12y – 8x dy dæ dz

A: To solve the triple integral

Q: What is the solution of 2r (y + 1) dr ydy 0 when z = 2 and y= 0 ? In(y +1) + 4 1- In(y+1) +3 In(y+1)…

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Q: 2.40 Solve the following problem for x (t) and y(t): x = -2x + 5y y = -6y - 4x + 10us (1) x(0)=5…

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Q: 1- If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8-3y) =x + c 3 a

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Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.