(1 point) Find the solution to initial value problem d?y dy 12 + 36y = 0, y(0) = 8, y'(0) = 6 dt dt? The solution is|

Q: Find dy/dt.

A: Given, y=9-4x3+2x; dxdt=-1,x=-3 To find dydt

Q: dt = (c) (9+t2)3/2

A: Given:

Q: general equation of (z-t)dz=(z+t)dt

A:

Q: Solve dy = 21( y² + 9) dt. 1. x² + y° Solve y'= xy 2.

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Q: 4) Equation: 4x +9y² = 1 1 Given that dy/ dt =8, find dx / dt when (x,y)= 3 9

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Q: 1 y" + (у)? %3D уу' у(0) %3D 1, у'(0) -

A:

Q: f(t) dt = x° – x“ + 2x² – 2 , x >1. 1

A: Given∫1x2ftdt=x6-x4+2x2-2∫1x2ftdt=t3-t2+2t1x2⇒∫ftdt=t3-t2+2tDifferentiating with respect to t we…

Q: the st sub: Z = the + 4x = x²(4t + 3), x(1) = 4.

A: Given differential equationAssume

Q: Solve 12 dy dy ty = t®y=1 dt

A: A differential eqaution of the form y'+p(x) y=q(x) yn, n ∈ℝ is called a Bernoulli differential…

Q: Problem 4: Solve d'y 9. dt2 dy (3) + T?y = 0, y(3) = 2, dt = -T

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Q: (1 point) Solve the following initial value problem: d 5 18e³t 12 1/² = (₁-3)* + (1960) 67²), 7(0) =…

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: (1 point) Solve the following initial value problem: dy + 3y = 3t dt %3D with y(1) = 3. (Find y as a…

A: To solve the following initial value problem

Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

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Q: t2-6t+9 dy 3. y = 2-5t+6' dt (t+1)(t²–1) dw 4. w = t2+2t+1 dt

A: follow next step

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: Q2: (a): Solve (i) (x² D² – xD – 151I)y = 0 y(1) = 0.1, y'(1) = -4.5 (ii) 100 – 20 + d? N dN dt? dt

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Q: x A(x) = † (3-1²) dt 0

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Q: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

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Q: dx? + (m – 1)(ax³ +b+ cy) = 0 dt2 How do you split this into 2 first order derivatives? Also what is…

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Q: Let F(x) = X S 12 Enter the exact answers. (a) F(12) = i (b) F' (12) = 2 √² + 25 dt. Find the…

A: Let . To find the following.

Q: dy dt = = -2y + 8(t-3) + 2H(t-4), y(0) = 1.

A:

Q: Solve the IVP explicitly: (2x + 6) dx/dt = −tsin(t2)          x(0) = −4

A: NOTE: Refresh your page if you can't see any equations. .

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: Find the solution to the initial-value problem dy dx 3xy(3+y), y(0) = 10 у),

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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.