1. Solve the IVP. (xy2 + 3y2)dy-2xdx = 0 y(-4)=-3/18 2. Solve the IVP. y" +2y+2y=8(t- -플) y(0) = 3, y'(0) = = 0 3. Solve the IVP. Answer in explicit form. State the interval of validity for your solution. x dy sin.x +2y = dx x y(2) = 1 4. 5. Use the method of Frobenius about the regular singular point x = 0 to find the indicial roots and recurrence relation for each root. 2xy" +y+y=0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. b. Determine the equation of motion. Determine the first time (after t = 0) when the mass first passes through equilibrium. Solve the IVP. 6. y" - 8y' + 15y = 9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. 8. x²y" 2y 3x² - 1 = x>0 Find the general solution of the ODE. y" +2y-24y: 12x+9-e4x = 9. Solve the IVP. y"" + 12y" + 36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = −7 1

Q: 7. y - y = 16

A: The objective is to find the general solution .

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Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 2 Solve for y. 3y-9 y = y+12

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Q: Find the solution. y'• ty ty" © y- (1-c, y- - (1-co")

A: We have to solve y'+ty=ty3 This can be written as: y'+ty=ty3⇒1y3y'+tyy3=t⇒1y3y'+ty2=t⇒1y3dydt+ty2=t…

Q: B. Solve y' + = y²x*.

A: the given differential equation is: y'+4yx=y2x3 the differential equation can be written as:…

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Q: 11. y = 5 3 * tn() 15 2x А. Inin 8 (35 С. Inin 15 (3" g") 2/x В. 15)(15) D.

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Q: 5) Solve y) - 3y4+3y" - 3y" +2y' = 0.

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Q: 7. (x − x² - y²)dx + (y + x² + y²)dy = 0. -

A: As students asked to solve only question 7. So we solve only 7th question.    In this question,  we…

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A: To solve the equation for x and y.

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Q: y'+Sy +b4= x²eX Sin5x Find the general solution of the equation.

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Q: Solve 6 Only Solve each equation by the method of inspection or any other method.

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Q: Find the solution. y'+ ty = ty3

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Q: Find y'". y = - 3x° (5x + 6)? O A. - 330x5 -1,800x4 - 60x .3 O B. - 3,150x5 - 5,400x4 - 2,160x3 OC.…

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Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

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Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: 1. Find the solution of the d.e. x²y" - 2xy' + 2y = 4x³ which passes through the point (1,4) with…

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Q: Determine the value of k that will make y = 2cos(2x) a solution to ky - y" = y. Ok = 5 Ok=0 Ok = -3…

A: Step 1:​y=2cos(2x) is a solution of ky−y′′=y.​Step…

Q: Solve y" - 2y" - y' + 2y = 0. Include a plot of the solution curves.

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Q: .3 t +y3

A: Derivative is below

Q: z

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Q: Find y'. 9) y = (5x-2)(3x + 1)

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