Find a solution of dy (x³ – 1) = y2 – 4 | dx that passes through the indicated points. a) (0,1) b) (0,0) c) G5 d) (2,)

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

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Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: dy 2х + ху is separable. dx y2 + 1

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Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

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Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

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Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: dy In(5a + 2) Find for y = %3D dx

A: Giveny=ln(5x+2)7e5xdifferentiate…

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

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Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: 3. Evaluate the line integral sin(y) dx + (x cos(y) – sin(y)) dy, where C is the straight line from…

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Q: dx-(it 2x tany) dy-0

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Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: Can i get help step by step please

A: To find dx/dt when y = 2 and dy/dt = 5

Q: 3) Find dy/dx Cas %3D X-

A: Given:

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Compute ∫C y dx + xy dy if C goes from (0, 0) to (1, 2) along the line parameterized as x = t, y =…

A: Here I am attaching image so that you understand each and every step.

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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