z=9x +4y + 1 dy (9x+4y+ 1)2 reduces to dx Using the substitution , the DE dz=9dx + 4dy (A) dz= (9 +z?) dx (B (4+z?) dz = dx dz = (4 +z?)dx (D (9+z?) dz = dx

Q: 1) f(x) = *+x*, r<1 x'+1 x21 df = ?, x1 dx a) f'(x) = %3! b) f'(1) = dx I = ?

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Q: FIND dy AND dy OF x= VI-t AMD y= t° -st. dx a 4t Vit day dx2 7-1^7- d^y-4t %3D c.)dy – 4t JI-t %3D –…

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Q: Compute dy/dx for y=u 3/2 and u=2x+5 using the chain rule formula dy/dx=dy/du du/dx. The answer is ?

A: The derivative of a function is a measure of the rate of change of the function with respect to…

Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

A: The given differential equation is x+2y-4dx-(2x+y-5)dy=0. We have to obtain the points of…

Q: 1. SE-0) dx =- SE-D) dx 4 In|x| +C А. 4x %3D 8. В. 4* _2. dx = 6Vx + C %3D С. 4 3. s(3V+) dx = (x…

A: Disclaimer: Since you have asked multiple questions, we will solve the first three questions for…

Q: SE-D) dx =- 4 In|x| +C 1. A. 4x В. 4* SA dx = 6Vĩ + c S(3Vx + dx = x + 3) + C 2. С. 4 3. D. -dx =…

A: Topic:- derivatives  Note:- as per our guideline if more than one question uploaded than only first…

Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D…

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Q: X - X UIS dx ? %3D 22n „(1-)3 (e) (2n).(2n)! I=u (c) (-1)" (2n+1).(2n+1)! -3 (P) I=u I=u 2n K (a)…

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Q: dy of x3 +v³ = 4 of X + dx Find O x? y² ,2

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

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Q: ·+w +z = 4 denklem sisteminin çözümünde z(x) =? dz - 4z = 5e* dx dx +

A: The differential equation is given as dzdx+w+z = 4…

Q: 2) I= ye-' dy Find :- a) 1= x eax" dx Q1: Answer of all branche 2) 1= yie dy 3) I x'e-dx -2x 1= J

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Q: (x In x)³ dx, (c) S Vin (1/z) dz. 9.33. Evaluate (a) (In x)* dz, (b)

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Q: 12. Evaluate (2+ r+3|) dx by interpreting it in terms of areas. Y-3+ 1-4 +3 %3D 2. a dy X dr t 3 dk…

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Q: x1/2 dx reduces to Using an appropriate algebraic substitution, the integral 1+x32 2y2 dy 1+y3 ys dy…

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Q: e-3x-1 In y dy – ye*dx = 0 o 2 (In y)² – e4x+1 = c In y? + e** = c %3D In y² – e4x+1 = c 2(In y)² –…

A: Here we have to solve the given differential equation

Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

A: Here I am attaching image so that you understand each and every step.

Q: 6. (4x'y? - 3) dx + (2x"y) dy = 0, y(2) = 4 7. x dy + y dx = 0; y(1) = -1 8. y dx + (3xy? + 2e") dy…

A: According to our company guidelines we must do only first three parts of questions if question…

Q: d²y 3- 33+ 10y = 0 dx3 dx? dx

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Q: 2x-x ca ch(y) 3 dy dx = 3 dx dy, then If (A)5, 0 2a+g(1)+2h(0)=

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Q: 3 Q 2x+2 dy dx dz in the order dz dx dy 0 -1 3 Q 2x+2 2 0 3 dy dx dz = ! J Į dz dx dy = 0 y-2 0…

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Q: dy +y When reduced to a linear DE of order one in z, the Bernoulli's equation |=3x?y? becomes dz (A…

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Q: dy %3D 1. If x'+ xy-3y' 10, then dx %3D

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Q: hat is the answer for this DE? 1.) (2x - y) dx + (4x + y - 6) dy = 0

A: We need to find the solution of the DE(2x - y) dx + (4x + y - 6) dy = 0

Q: dy Q1/ Find dx 1. if y = u and u 4x2-2x +5. %3D 2. y = (x2 + 4)2(2x3- 1)3 %3D 3. xy + x- 2y- 1 = 0…

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Q: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

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Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…

A: Find the derivative

Q: dy et + 4x Find if y = The answers have been slightly simplified. %3D dx 3x – 1 (3x – 1) (e² + 4) +3…

A: The given equation is y=ex+4x3x-1.

Q: ed²y "-xy+e*(1+ 2x) = 0. dx? dy 6. (a) If y = e¯* In x , find Then show that x dx

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: Given; √ √ tex dx 2 Applying rationalizing substitution, find dx in terms (A) z dz 2+z² 2 z dz B…

A: Given query is to find the dx in terms of dz.

Q: r1 -x²-y² •1 p? sin ф dp dф d@ 1+ p2 dz dy dx is equivalent to 1+ x2 + y? + z2

A: This is a method of solving integral by converting cartesian coordinates into spherical coordinates.…

Q: dx O a. dy -3y2+2x 2x +2y 2x +2y -3y +2x O. dy 3y2 - 2x 2x+2y -2x-2y dx -3y +2x %3D dx O b. dy dx dx…

A: Given query is to find the derivative of the expression.

Q: dy If y = x- xy +1, then when x = 1, is dx 2-0 2-2 O nonexistent 1/2 1/2

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Q: S x dx/(x² - 3) = In]x? - 3| + c * %3D O False O true If y= csch3x then dy/dx = - 3 csch3x %3D…

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Q: 1 c2(1-z) Evaluate Sa-2) s(1-;-2) dy dx dz

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Q: z=cos y Using the substitutions the DE (3cos y – 5x)dx – 2x?tan y dy =0 reduces to dz = - sin y dy A…

A: Using given substitution.

Q: -2 Given that dx = In|x + 1| – In|x – 1| +c ,find dx = (a) In9 (b) In4 (c)-In4 (d) -In3 (e) None

A: Given, ∫-2dxx2-1=lnx+1-lnx-1+c

Q: dy =cos (x- y), use the substitutions dx To solve the DE (А) z= cos x- cos y; dz= - sin x dx + sin y…

A: topic - differential equation answer  option C  z= x-y ; dz=dx-dy

Q: dy in term of x and y if Find dx (a) y +6x=x² (b) y-cos y=x+sinx (c) x² +4xy+3y² =3 %3D (d) 3y…

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Q: dy If the substitution m = y-x was applied to the DE: dr 1- 3(y- a), the resulting DE would be: dm -…

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Q: 4e4sin6x dx secбx Evaluate A) -In|sec6x| + C B 4sin6x + C 1 e4sin6x+ D 4In|sec6x| + C

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Q: 1. ху' %3D у + уx? — у? d²y 2. х- dx² = 2-a dy dx 3. Зуу'у" — у'3 +1%3D0

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Q: II Sohe for dy/dx 1. y- (x2-4)+2 (x+3) x'y + xy2 = Jx-y -3 5x- 3 4-3X 3. y= () 2. %3D 4. Y= J1-t2…

A: We know that derivative of xn  is  d(xn)/dx = nxn-1. And d(√x)/dx = 1/(2√x). And d(U.V) = U'V + V'U…

Q: 8) What is dy/dx of ye² = xy? y-ye a) y = ez-x y+yx b) y= 2 c) Y = d) y = e" -x e) None of the above

A: Given,  yex = xy  So, differentiating both sides with respect to x, We get,

Q: dy If y=Vx +1, then is dx 1 A (x² + 1)³/2 B x(x² +1)/2 В x² +1 1 D x² + 1 E None of the given…

A: we have to differentiate the following

Q: d²y dy dy %3D 1 2. dx2 6y = 0, when x - 0, y = 2, - %3D dx dx

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Q: -2 dx Inx+1|-In|x-1 +c ,find -2 dx 3D 2-1 Given that (a) In9 (b) In4 (c-In4 (d) -In3 (e) None O a e

A: Let's find.

Q: (e* + у) dx + (2 + х+ yev") dy %3D0 ; У (0) 3D 1 а. b. (4y + 2x - 5) dx + (бу + 4x —- 1) dy %3D 0;…

A: The given problem is to solve the given ordinary differential equations, we have to check the…

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming A B © ² с -dz 1+z² © S²+ /…

A: Please see the answer below.