If y = f(x) is the solution of y" – 8y' + 16y = e5z, f(0) = 1, f'(0) = 5, then %3D Lütfen birini seçin: O a. All the previous answers are not correct. O b. f(1) = e3 c. f(1) = ev O d. f(1) = e O e f(1) = e

Q: 2/3' 2/2, Suppose 3z? + 2y² + z² = 1 and z = g(x, y) > 0. Determine g, ) and gy 2/3' 2/2

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Q: 25 12 8. x' = | 6. -18 -5 %3D 6 13

A: First we will find the eigenvalues and eigenvector of the given coefficient matrix then we will form…

Q: 1. Find the general solution of (x³ + 3y)dx – xdy = 0 x³(x² + C) x³(x² + C) a. y = - 2 b. y =· 2…

A: We have to find solution

Q: Let f(x)=2+x22−x3 , then f′(1)

A: fx=2+x22−x3Differentiate w.r.t. "x",f'x=0+22x21−3x2f'x=22x21−3x2

Q: 1 If = 1/2 = = a + b and ¹ = a - b, then x - y is equal to: x y

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

Q: / Does the following equation satisfied Cauchy-Riemann's equation. (w=z

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Q: Find the general solution of the D.E. y(2y+ 4x – 2)dx – 2(x+ y)dy = 0. a. 2xy + y? = ce-3* c. 2xy +…

A: Use integrating factor method

Q: 2xydy + (y- 3x-)dx = 0;y(3) = 2 O xy² - x³ = c O x³ 2 – xy² = -15 Ox* - xy? = 15 O x³- xy? = c

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Q: Find a general solution for x³y' + 2x²y = 3; y(1) = 12. %3D

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by x3 compare this DE…

Q: 1 Separate variables to find a solution a. yy' +36x=0 b. y'=1+4y², y(1) = 0

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Q: 15. Obtain general solution of y' = y + y³. a. y² = 1 + ce²x b. y2-1/2 + ce²x c. y2=1+ ce-2x d.…

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Q: If h(x) = x" for some positive constant a, and h(27x) = 3h(x) for all positive value of x, what is…

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

Q: 4. Solve for the general solution of --y = x²y? a. y-1 = Ce* - 12e* b. y-1 = Cex - 10e2x c. y-1 =…

A: Given that, The differential equation is following, dydx-2xy=x2y2 We have to find the general…

Q: (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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Q: (0) = 2 is

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Q: 4. Write the solution of i = -y, ý = x, x(0) = 1, y(0) = 0 %3D

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Q: Suppose a company that makes lava lamps is trying to determine how to increase profit.  They find…

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Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

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Q: If y = f(x) is the solution of (18x?y + 2x)dx + (6x – 108y?)dy = 0, f(0) = -1, then Lütfen birini…

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: Find y' and y". 1. x3 + y2 – 3x - y- 6 = 0

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Q: 3ydx – xdy = 2y4 dy, y(0) = 1 a. (11x – 2y^)3 – 8y = 0 b. (11x – 2y“)3 + 8y = 0 c. (11x +2y“)3 – 8y…

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Q: Find y' if xy = yx. y' =

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Q: Solve the problem y' = x²y², y(0) h = 0. 1. Select the correct answer. = 1 numerically for y(0. 2)…

A: Euler's Method is used

Q: dy Find the solution of the Bernoulli's equation x + 6y = 3xy4/3. dx 1 1 а. у b. y (x2+cx)3 (x+c)3 1…

A: We solve by Bernoulli's equation.

Q: dy The general solution for y) dx OA. y = c1+ Cze* В. x. y = C1+ C2e* y = e* + 1 D. y = C1x+ c2

A: Given differential equation is d2ydx2-dydx=0 The given equation can be written as D2-Dy=0 Where…

Q: 2xdy + y(2 + xy²)dx = 0 %3D 1 when x = 1 & y= 2

A: Given equation is 2xdy+y(2+xy2)dx=0 and y(1)=1/2

Q: Given y = (u² + 1), u = x² = 5, determine when x = dx - 2.

A:

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.