Test V. Solve for IVP. d²p{t) 1. +4 dp(t) + 4 p(t) = 2e¬t; p(0) = 0; p'(0) = 0 %3D dt² dt %3D

Q: 2 3/2 between x = 0 and x = 1 is 3 %3D The length of the curve y =

A: We will find out the length of curve.

Q: Vx6+7 (etan**) dy where ylny) = dx B) find (x2/3)( y v) sec

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Q: Solve x+ ye dr- xe dy = 0, y(1) = 0 %3D

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Q: (ve" + 2u) du + e"dv=0|

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Q: Verify the exactness of the given function (1+ex/y)dx+ex/y(1-x/y)dy=0 and then write the complete…

A: Solution: The objective is to find the general solution of the given differential equation

Q: Compute dy / dx and d2y / dx2              x 2 - 4y 2 = 8

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: dy dx Find when 6x2 + 3x3y - 3y2 - - 58.

A: 6x2+3x3y−3y2=58

Q: y = V3x² + 6.

A:

Q: Find dy/dx. x = t /2 + t y = sqrt(2 + t

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Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: (y² + 1)(x + 1)dy = (y² + 3y)dx → Variable Sep.

A: The solution of a differential equation is defined as the function which satisfies the differential…

Q: Solve the followi ing

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: dy +x? = 1 dx %3D

A:

Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: dx -y = 5 dt dy = 3t dt 2x -

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Q: dy Find for 3(x2 + y²) ² = 100xy dx

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Q: Solve (Vr) = sec (Vx) using variable separable form. dy dx

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Q: x(3-5x) 2. dx (3x- 1)(x – 1)²

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Q: Solve: dy/dx = 2 + sqrt(y - x+ 3). %3D

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Q: Solve y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0 using the substitution Z = 2 x y

A: Given that y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0  Therefore, we have  y (1 + 2 x y) dx + x (1 – 2 x…

Q: dy - x X, y(0) = -4 dx Need Help? Watch It

A: using variable separable and then integrate both side...

Q: d'y as a function of t if x t+ (a + B) (a+ B) (a) Find , y=t- t (6) t

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Q: dy d²y Find аnd dx the first and second derivatives, for #2 & 3: dx2 • 2. y = 2x2 + 3x + 1 3. y =…

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Q: find dy/dx if x=(t2-2t+1)e3t and y=(t2+4t+4)e3t

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Q: y= In]3x+2)²/2x–1 dy 1. Find dx

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Q: | x² J1(2x) dx , (use subsitution)

A: Bessel function in terms of series is Jn(x)=∑k=0∞ (-1)kk! γ(n+k+1) x2n+2k. We will prove the…

Q: Differentiate. 4t f(t) 9 + t2 f'(t) = %3D

A: To differentiate the given function.