(1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

Q: j Find y as a function of æ if a?y" – 9xy' + 25y = xº, (1) — 2, У(1) — -5. y =

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Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: Derivative of y = 16 is: a) 1 b) 0 Derivative of f(x) = - 6x + 2 is: a) - 4 b) 2 Derivative of g(x)…

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: V omain h e Range -3 Da a

A: A function is a relation which describes that there should be only one output for each input every…

Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

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Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

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Q: |(0,3) C1:x2 + y? = 9. (-3,0) C2 (3,0) Figure 1 Based on Figure 1 and given that F = y²i + (3xy +…

A: We have to find the work done by the vector force F =y2i+(3xy+4x)j Where c is a smooth circle…

Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: If f(2) = (3z)²a² z+2/a find and simplify f(/@). %3D

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Q: Chioma was asked to find (18x + 3)(6x° + 3x)° dx using u-substitution. How should Chioma define u?…

A: ∫(18x2 + 3)(6x3 + 3x)6dx We have to use u-substitution for the above function. To solve this, u is…

Q: 5 B) Find y" for the function y = x + Vx at p(1,3)

A: Given query is to find the double derivative of the expression at point p.

Q: The value of 'a', for which u(x, y) = xt + ax?y2 + y is a harmonic function, is

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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.