4. Solve the particular solution of the given D.E using the provided initial value condition: (1+ a*)dy+ x(1+4y² )dæ = 0 y(1) = 0

Q: Find an explicit solution of the given initial-value problem. dx dt 8(x² + 1), ×(Z) = 1 4

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Q: Solve the initial-value problem (4y−cos y) dy /dx −3x2 = 0, y(0) = 0

A: 4y-cosydydx-3x2=0 On simplification, we get ⇒4y-cosydydx=3x2⇒4y-cosy dy=3x2 dx Now integrating on…

Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. dy 1 1, 01

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Q: 2. Solve the initial-boundary value problem du 3 au 0 0 10 Əx? ди (0, t) ди (4т, t) — 0 t >0 0, 0 <…

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Q: Solve the initial value problems d3r/dt3 = -cos t; r''(0) = r'(0) = 0, r (0) = -1

A: Given: Initial Value problem To Find: Solution of the above differential equation

Q: 3. Find an explicit solution of the given initial-value problem. dx 4(x+ 1), x(7|4) = 1 2 dy y sin…

A: 1. The given differential equation is a separable differential equation, so find the solution of it…

Q: 1. (t + 2)y' + In(t + 4)y = 5t, y(-3) = -2 Find the interval in which the solution of the initial…

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Q: The function f (x) = e-® + 1 is a solution to the initial-value dy problem dx 1 -, y (0) = 1. True…

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Q: 1. Solve the stochastic differential equation. Hint: Y, = VX,. %3D dX = X;* dt + X dB, %3D

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Q: Find an explicit solution of the given initial-value problem. dx 8(x2 + 1), dt IT 1 %3D 4

A: We need to find explicit solution.

Q: 5. Find the solution of the given initial value problem. ty' + (t + 1)y = t, y(ln 2) = 1, t > 0

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Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) = 0, y'(0) = 0, y"(0) = 3. %3!

A: The differential equation is y'''+4y''+5y'+2y=10 cos t , y0=0,y'0=0,y''0=3. The general solution of…

Q: dy 2 %3D

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Q: 23. The solution of the initial value problem y dt + (2y² + 1) (cos t)?dy = 0, y(0) = 1 is %3D

A: The given equation is: ydt+2y2+1cost2dy=0 and the initial condition is  y0=1. To find the solution…

Q: Show that the initial-value problem 1+x 1+t' 0≤t≤ 1, x(0) = 1, is well-posed on D = {(t, x) |0 ≤ t ≤…

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Q: Find the general solution of the first order differential equation dy = 8x +1 and the particular…

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Q: 2. Verify that y = -t cos t – t is a solution of the initial-value problem dy = y + t²sin t dt y(7)…

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Q: Find the solution to the initial-boundary value problem: 2u Əx² » du 0 0, t > 0, du (0, t) = (1, t)…

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Q: Proceed as in Example 6 in Section 2.3 to solve the given initial-value problem. S 1, 0sx s 1 x > 1…

A: Given that dydx+y=fx  , y0=1  fx=1  ,0≤x≤1-1    x&gt;1Solution:When 0≤x≤1dydx+y=1 this is the linear…

Q: Find an explicit solution of the given initial-value problem. dx dt = 7(x² + 1), x(7) = 1 X ||

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Q: solve the initial-value problem. dW/dt= e-4t, for t is greater than or equal to 0 with W(0)=5

A: We solve the differential equation by variable separation method

Q: dy (x + 1)+ y = In x ;y(1) = 0 %3D

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Q: Solve the initial-value problem. 3 dy + 3t²y = 2 cos(t), y(¹) = 0 dt

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Q: Find an explicit solution to the initial value problem: dy = dx y(x) = ex - 5y y(0) = 0

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Q: Determine whether the initial value problem y′ = cos(t + y), y(t_0) = y_0 has a unique solution…

A: This is a problem of IVP.

Q: Find an explicit solution of the given initial-value problem. dx - 3(x² + 1), xG) = 1 dt

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Q: Find an explicit solution of the given initial-value problem. (1 + x*) dy + x(1 + 4y2) dx = 0, y(1)…

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Q: 2. Solve the initial value-problem: . dY dt Y with Y(0) = (1,0). - 4

A: The solution is given as

Q: Consider the initial-value problem ay" + by' + cy = g(x); y(xo) = 0, s/(x0) = s6- Suppose that the…

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Q: Find the particular solution of the differential equation dP − kP dt = 0 that satisfies the initial…

A: the given differential equation is: dP-kPdt=0 the initial condition is: P(0)=P0. we have to find the…

Q: 2. Find the solution of the given initial value problem using MUC: 2y(3) + 5y(2) + 6y(1) + 2y = e-3x…

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Q: Find an explicit solution of the given initial-value problem. (1 + x4) dy + x(1 + 4y2) dx = 0, y(1)…

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Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) 0, y'(0) = 0, y"(0) = 3.

A: SOLUTION-

Q: Find explicit particular solutions of the initial value problems in Problem dy : бе 2х-у, у(0) %3D0…

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Q: Find the solution of the initial value problem. dy y - 2, y(0)=3 dt 1+t

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Q: Find an explicit solution of the given initial-value problem. dy_y²_ 1 = y(4) = 4 dx 1 ||

A: The objective of the question is determine solve the differential equation.

Q: Q3: Determine the solution for the following initial-value problems: d²y dt2 + 4y = 2cos t, y(0) =…

A: We have to find the solution

Q: Find an explicit solution of the given initial-value problem. (1 + x²) dy + x(1 + 4y²) dx = 0, y(1)…

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Q: Find the exact solution y to the initial-value problem dy = zy/2, dr y(1) = 4.

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Q: Find an explicit solution of the given initial-value problem. dx = · 3(x² +1), x(7) = 1 dt X =

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Q: y"" − 4y=et+t, y (0) = y'(0) = y" (0) = 0 C

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Q: Solve the given initial-value problem by finding, as in Example 4 of Section 2.4, an appropriate…

A: Here, the given DE is: (x2+y2-7)dx=(y+xy)dy⇒(x2+y2-7)dx-(y+xy)dy=0...(1) Now, Comparing it with M…

Q: Solve the given initial-value problem. dx1 X, (t) with x, (0) = - 1 and x2(0) = - 2. X2 (t) dt 4 7 -…

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Q: 1. Find the solution of the given initial-value problem: dy + 6 + 8y = e, y(0) = y'(0) = 0. di? dy…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Consider the initial value problem u′(t)+u(t)=(u(t))3,u(0)=1/√2 Although the differential equation…

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Q: 3. Find the solution of the given initial value problem. dy y = xe", y(1) = e – 1, x > 1 | dx

A: I am attaching the solution of question (3) only.  The solution is, y = x(ex - 1)  The detailed…

Q: Find the solution of the initial value problem dy =Vx + x, dr у (4) - 0

A: ∫xndx=xn+1n+1+C

Q: 2. Solve the initial value problem, if it is exact: (4y+2t – 5)dt+(6y+4t–1)dy = 0, y(-1) = 2.

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Q: Find an explicit solution of the given initial-value problem. dx/dt = 7(x2 + 1),    x x(?/4) = 1

A: Given an initial value problem : dxdt=7x2+1 Also x(4)=1 We need to find an explicit solution. Let's…

Q: Find an explicit solution of the given initial-value problem. dy y (2) = 2 %3D dx x2-1

A: An equation which involves the derivative or differential coefficient is called differential…