1 Q 2. Differentiate h(x) = (V+ -2 IX

Q: 16. Find all values of the constant c so that (xy + 1)dydx = 4 + 4c. -1J0

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Q: 2. Eliminate the arbitrary constant on the given equation: y = C₁e-²x + De4x

A: Given  y=C1e-2x+De4x

Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: Ⓒ Solve зик subject to + 2x x = 0 u(x,0) = in Rx [0,00) n(x)

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Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

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Q: O ) -. x- -2 46. f(z) = 1/x. - -2 fe) = V3r + 1, x=0

A: Given: 44.  f(x)=x2,  x=−246.  f(x)=1x,  x=−248.  f(x)=3x+1,  x=0

Q: (a) J (x+1)2 d.x. (b) ST-1y 1)(n²+1)² dax.

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Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: Solve y" + 2y' + 2y = g(t), y(0) = 0, y'(0) = 1, where %3D %3D S1 0 0 27 T <t< 2m g(t) =

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

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Q: x°y"+ 2x?y"+ xy'- y=0

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Q: (금)시 3 k dt t2 (5 – 5t)i + 4/tj+ -

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: 31 Solve by the Method of Variation of Parameters: y" – 3 y' + 2y = cos e t

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Q: se the method of variation of parameters to determine a particular solution to the given equation.…

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Q: 8 2 f(x)dx -43, then | f(t)dt = If 8.

A: Given By the property of definite integral, we have

Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: L[(t + 1)2e] = ? %3D s2-1 s2 +1 (s-1)2 (s – 1)2 -

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: 41n <ys 28 31r x = sec* (7t) – 1dt, | 21 41x 28

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Q: Q2: If Z1= 4i-3 22= 3i Z1+Z2 Find Z2 (2x² x > 2 Q3: if f(x) = 4 x < 2 f(x)dx

A: For question 2 given data is   and for question 3 given data is…

Q: /2 ( 2) (2a- z) dr x2) ? dx • B I A , E E E E 8 &

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Q: Q: Solve : ー4t y"+2y - Sy dt = e s(t-3) 1リ %3D yco) = 0 っy c0=0 (0) = 0

A: We have to calculate function from the given question.

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: 4y"-y=e^x/2+6 consider the following DE to be solved by variation of parameters

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Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

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Q: 2 O Finel F.S For Fex) = 2くxくだ 7. %3D 2. -2 37 2 2.

A: By Bartleby policy I have to solve first question, as these are all unrelated problems. These are…

Q: .3 S(3 – e3*)²dx

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Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: (b) Consider the IVP, test whether it is exact and solve it. x(x – y)dy = -(3xy – y²)dx y(-1) = 1

A: Given differential equation x(x-y)dy= -(3xy-y2)dx   To test exact or not ,if it is exact then solve…

Q: Q/ Solve the differential equeion tx²y)dy=2xydx

A: The Given differential equation is: (x2-y2)dy = 2xy dx Rearranging the differential equation:…

Q: 3. p + y = ty dt dy 2ty(y – 1) dt 6. 3(1 + ²) %3D

A: Given 3 t2dydt+y2=ty6 31+t2dydt=2tyy3-1

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: Assume that a factory can produce a quantity 2x3 + x°y + y4 of goods, when x is skilled workers, and…

A: Here we use the concept of implicit differentiation.

Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

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Q: (1+ t?)ds + 2t [ st² – 3(1+ t²)²]dt = 0 t = 0; s = 2 %3D

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Q: |z"e*dz =T(n+1) = n!

A: The gamma function is defined as ∫0∞tn-1e-tdt=τ(n)=n-1!           (1) the given integral is…

Q: 2 dt t² +2t +3 18. Evaluate 8 dz z² +8z+ 25 20. Evaluate o

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Q: L(cosh 4t) = %3D s²+16 .b O s²-16 .C s2 – 4 I. .d O s2 - 8 SI

A: We will find Laplace transform of Cos hyperbolic function

Q: (14) f (x,y)=e" (x² +y²)

A: f(x,y) = (x^2+y^2)e^-y fx= 2xe^-y fy= -(e^-y)(x^2+y^2)+ 2ye^-y fxx = 2e^-y fyy = (e^-y)(x^2+y^2)…

Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: H.w Solve y'+y'-zy= -2 f yoj=Zfylcojal

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Q: 2. Solve the IVP: *+ 2y = te-2", y(1) = 0 dt

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Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows: