Find the Wronskian for the differential equation dy dy. +7 + 12y = 0 dx2 d.x .A -Ze-7x .B 7x .C -3x -4x y= Ae¯3X + Be .D -7x -e

Q: ·S√2t³t² dt = dr 8 √2x³ - x²

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Q: Evaluate. The differential is exact. (1, 1, 1) (-10x - 8x7y7) dx - 7xS6 dy + 54z5 dz (0, 0, 0) 3 4

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Q: d²y 2. Find the second derivative, dx² a. x = t² + 1 and y = t³ b. x = - t2 + 2 and y = sin(t+ 1)

A: Let's find.

Q: 2. x²y² = 3y' +1 dy %3D dx

A: Please refer the attached image for complete solution.

Q: d²y dy 6. 2+ 8y = e-3x dx 1. Solve dx²

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Q: Solve the given equation.. dy - 3y = x³, v(1) = 10 X dx a. y(x)= x²Inx+5x³ b. v(x)= x?Inx + 10x³ c.…

A: Please refer to the image below

Q: H3. Solve the following differential equations dy 1) 2) d²y dx² +4+4y=x²²e-²x, dx d²y dy -6 +9y=e³x…

A: Sol:- 1) y'' +4y' +4y=x-2e-2xy'' +4y' +4y=e-2xx2The general solution to axy''+bxy'+cxy=gx can be…

Q: D7. Determine the oscillation of "-tx² + x = 0.

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Q: (2y* + 42) dx = (6² – 2xy²) dy -

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Q: dy Which is the of the equation y = e 2x +3? dx 2 В. х+ 3 С. 2х + 3 O x + 3 2X + 3 2e 2x+3 Option 4

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Q: x² + 4y² = C(x+y)

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Q: Find the Wronskian for the differential equation dy dy 3- - 10y = 0 d.x - - dx? .A -3e30 .B 3e-3x .C…

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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: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. O B. O U ev O D.y O E.…

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Q: у (4х + у) da 2 (x² – y) dy - - 2x2 + x + 2 ln y = C ans.

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Q: d³y 1. dx³ dy + 6у — 0 dx dx²

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Q: Differentiate. g(t) =  5 − 7t 8t + 9 g′(t) =

A: solution: the objective is to find the derivative of the given function

Q: Solve the given equation.. dy dx a. + 2xy = x, y(0) = -2 C. y(x)= xex-2e-x² ex-5e-x² 2 b. y(x) = 1/2…

A: The given equation is; dy/dx+2xy=x, y(0)=-2.

Q: y′ = − y(3 − ty)

A: Given that

Q: Find an expression for dy/dx. y = u? and u = 3x - 1 18x 18x - 6 0 9x -3 O 6x - 3

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.