2 d y d y + dx? + y = e* dx?

Q: If y =Aem + Be nx d'y -(m+n) dx? dy + mny = 0 dx Show that

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Q: dy If e"y – y? = e – 4, then at x = and y = 2, 2 " dx - ||

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Q: Sclve th initial valu e probi dy + 2 . 3. dx3 dx? Y'c0) = 8 y"(0) = -4

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Q: dx from a = 0 to b = 1 et + e-

A: Integrals in some cases can be simplified to standard integrals with relevant substitution. For…

Q: 4x2 +y d'y when = 2 and y = 1. 17 then evaluate %3D dx? (Answer accurate to two decimal places.)

A: This question can be solved using the concept of second order derivative.

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: Evaluate L e* dx dy by using trapezoidal and Simpson's rules.

A: Given that, ∫02∫01ex+ydxdy By trapezoidal rule, ∫abf(x)dx≈h2f(a)+2fa+b2+f(b) where h=b-an…

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

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Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: Obtain the general solution of the equation d'y +6 dx dy ? + 10y = 50x dx %3D

A: Given : d2ydx2  + 6dydx+10y = 50 x

Q: The value of yx +y dx dy

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Q: Given ey = x + y. Show that x +y (x + y – 1)3 d?y dx?

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Q: EXAM Q1-If x= cot- VE, y =;, find dy dzy dx' dx2 at t = 2. t+1

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Q: Determine dx dy in terms of x and y for the equation x + xy? – y = 3.

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Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: Sin JxCosx dx =? (e() b) fx'e dx=?

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

Q: angleO: Find a Tayler saries for Hhe Sunction fa)= In G) contered at a=I

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Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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Q: d?y dy I+ dx 13 What is the degree of the DE dx2 (А) з (B 1/2 2 D

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Q: Find the values of a and b that make following D. E is exact (-) dx + (xy + 1) dy =

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Q: Evaluate I = |e dx using trapezoidal & Simpson methods. take h= 0.5.

A: Given: The integral is  I=∫02e-x2dx and h = 0.5   To determine: The value of the integral I using…

Q: d?y What is the degree of the DE dy 3 dz 2 dx A 3 2 1/2

A: Degree: the degree of the differential equation is defined as the exponent of the highest order…

Q: d'y If xy + y' = 1, find the value of at 2 dx (0,1). %3D

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Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: y par e for JTx (inx)? dx. wtioni dv = %3D

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Q: 1. Given that Y = e + Cosx, find: dy a. dr b. d'y/dx?

A: Hello , thanks for your question but according to our policy I am answering the very first question…

Q: Which one is an exact equation? (Зуш? — 1) dar + (2a3 + 3у) dy — 0 2у(а + у + 2)dx + (у? — а? — 4г —…

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Q: (b) Given y = Ax + Ba?. Show that dy 2x- + 2y = 0. dx2 dx

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Q: II. Determine the order and degree of given DE d?y 1. dx2 = k[1+ dy/dx]³/2 Vdy/dx dx3 2.

A: Given Differential equation1.d2ydx2=k1+dydx32squaring on both…

Q: Find the order and degree of 1 d y 1+ dx3 d'y dx4 O Order=3, Degree=20 O Order=4, Degree=20 O…

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Q: dy d’y The order and degree of the DE + = 0 respectively, are and dx dx?

A: The order of a differential equation is the highest order derivative it contains. The degree of a…

Q: Evaluate |//.(a (x + y – 5z) dV where E = {(r, y, z) | - 4< y< 0,0 < I < y,0 < z < ¤ + y³} E Round…

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Q: dy is equal to- dx If y = !, then the value of +3 V1 +y* V1+x

A: Introduction :

Q: 17. y dx — (х + бу?) dy %3D 0

A: Given ydx-x+6y2dy=0          (i) To determine the solution of the given differential equation.

Q: dy Find dx at the point ( x, y ) = (1 , 0) If e *y = e * In(x²) + y² + 1 %3D

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Q: 些。x? dx z + 6 -4 y %3D хе ? dx4 with YLoI = 5,y'col =1, 9°co) --2 yiol e 007

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Q: Given x = 8 In(t) and y = 64 t² then find dy %3| dx d²y %3D dx? ||

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Q: Using dy = dx and dx = 0.03, what is dy when x = 2? %3D 2/3x – 2 dy = i (Write as an exact decimal.)…

A: Given that :- dy=323x-2dx dx=0.03 , x=2 , dy=?

Q: Find for dy dæ² y(x) = cot(x) *= csc? dy dx? 2

A: Given query is to find the double derivative of cotx.

Q: 1 In dx%3D %3D .a 3. m/2

A: Gamma function

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: 1 dx using the trapezoid rule with n=4 1+x d. Use your answers for parts a and b to estimate

A: Given the integration ∫0211+x3dx

Q: The value of [ yx? +y? dx dy %3D

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Q: dy What is the value of dx at the point (1,0) if y = In(x² + y²)? %3D Undefined O 1 O 2

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Q: arctan dA , where R = {(x,y)|1< x² + y? < 8, 0<ysx} %3D

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Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy (Write as an exact decimal.) %D

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Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: What is the general solution of ydx (* + Vy? - t²) dy %3D = cy arcsin In y = C %3D O arctan In y = C…

A: Convert this equation into the homogeneous differential equation.

Q: 1- y? 1+ y 4 06: If x? dx Show that 1 %3D ,2 dy レアス+1.

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