Consider the initial value problem: ty = −y+3t², y(1) = 0 (t > 0). Find the value of y(2).

Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: Find the linear approximation to f(x)=x2+1x−2 near a=3.

A: Given: f(x) = x2 +1x − 2; a = 3

Q: i(t) = (A₂ + A₁t)e-at

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Q: dK (t) The rate of net investment is given by dt (1 + 4t)e2t+4t + 12t/3 +t and the initial stock of…

A: we have to integrate with respect to t

Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

Q: y" – 2y' + y = -3 –x+x, y(0) = -2, y(0) = 1.

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: 9. At time t= 0 a particle is at the origin. It then begins moving along the positive x- axis so…

A: For part (a):

Q: dy Solve the initial value problem: + 2y = 6e¬x; y(0) = 8

A: Since the given differential equation is first order linear differential equation so we first find…

Q: How to solve this equation y'''-4y''+2y'-8y=6e^(x) - x^(2) + 1 using Methods of Undetermined…

A: Given: Given differential equation is y'''-4y''+2y'-8y=6ex-x2+1 We will solve this equation using…

Q: (b) Solve 1 y +-y= 0, t> 0. t

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Q: Solve the initial value problem: (3x + 8)(y² + 4)dx – 4y(x² + 5x + 6)dy = 0, y(1) = 2

A: A differential equation is said to be in separable form if it can be written in the form . Such a…

Q: Solve the following initial value problem: + 8y = 4t with y(1) = 4. (Find u as a function of t)

A: Consider the provided question,

Q: 2x³+1 2. Let g(r) = 1 dt. Use part I of the FTC to find a formula for g'(x). There is no need V3+ t2…

A: Given g(x)=∫-32x3+x13+t2dt

Q: The function y(t) = 4e³t - 2e5t is a solution (but not the general solution) to y" + py' + qy = 0.…

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Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: (7y+yt/t)=n Solve for y

A: The given expression 7y+ytt=n Solving further 7y+y=n8y=ny=n8

Q: Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y²…

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Q: 4. Aşağıdaki denklemi y(2)=1 başlangıç koşulu için çözünüz dy (x² + 1 ) + 4xy = x dx

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Q: Find the particular solution: y': 3(x² + √x) yez , y(4) = 0. ans

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Q: Find the solution of y" – y – 6y = 48 et with y(0) = 7 and y' (0) = 3.

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Q: Use the convolution to write a formula for problem: y" – 3y' + 2y = f(t), y(0) = 1, y'(0) = 0; -

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Q: Solve y² dt+ (2yt + 1) dy = 0

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