dy Vy³ - Vy (1–³Vy)

Q: dy 4xy+5y2 The DE: can be transformed into a seperable DE %3D dx xy +3x2 in x and z by using the…

A: We have given a differential equation and we have to find substitution to make it variable…

Q: Consider the ODE y In y dx - xdy =0 With initial condition: y(2) =e

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Q: Solve by Laplace Transform: y''+6y'+5y=e^t; y(0)=-1,y'(0)=2

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Q: dz If z = x.f(xy), express x - Y ze in its simplest form. CS Scanned with CamScanner

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Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

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Q: Solve using Laplace transform y" +y=t² +2, y(0)=1, y'(0)=-1

A: take Laplace here we have y(0)=1 and y'(0)=-1

Q: use the chain rule to find dy/dx y=(u+1)2;u=1-x

A: Given:The chain rule of differentiation states that:Applying the derivative with respect to x and…

Q: The special integrating factor of y'dx+(3xy + y² -1dy = 0 is: a. e3y b. Зу С. У d. y-3

A: Solution

Q: (2xy + x? + x+)dx – (1 + x?)dy = 0 -

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Q: dx using miscellaneous substitution will yield to secx + 1 Transforming Ⓒ S A 1-z² B 1+z² © √ 1 +…

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Q: dy _ 4xy+5y² can be transformed into a seperable DE The DE: dx xy +3x2 in x and z by using the…

A: The solution is given as

Q: Give the Laplace transform of the solution to y' + 3y-4 e* – 2 sin(2 x), y(0)=5]

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Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: SxY (@) = 0 and Sx (@) =0 if X(t) and Y(t) are orthogonal.

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Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: y' – 5y = e5x ;y(0) = 0 %3D

A: The give question is related with differential equation and Laplace transform. Given that,…

Q: The Integrating Fachor for the DE y dx- Ge-2x)Jdy -2y None of These

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Q: S dx secx + 1 Transforming Ⓒ / + A -dz 1+z² 2-2z² (B) 1+z² C 12²+2 dz Ⓒ √ 1+2²2 dz D 1-z² -dz using…

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

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Q: OSS T (x+y2) dydx

A: When the region of a double integral represents a circle, it is convenient to use polar coordinate…

Q: Use an appropriate form of the chain rule to find dz/dt 1. 2 3xy; a r-t' and y

A: use partial derivative for finding drivative.

Q: To reduce the DE (x+2y-4)dx-(2x+y-5)dy3D0 to a DE with homogeneous coefficients, use the…

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Q: solve the equation by Laplace transform. y'' - 3y' + 2y = exp(3t),  y(0) = 1, y'(0) = 0

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Q: dx Use the chain rule to find () in terms of x and y dy 2 y = ( and X = t2 at t= 2

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Q: Determine the of : In (xy²) = x y dx

A: Derivative dydx of equation  lnxy2=xy

Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: If f (x, y) = 4e4*cos (y - 1) , then the linear approximation at (0, 1) is %3D (A) 4+ 16x (B) 4+4x…

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Q: Solve using Laplace transforms y''+2y'-6y=7e-3t, where y(0)=1, and y'(0)=-2

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Q: Find the Laplace transform; y''+y'+3y=e^-3t y'(0)=y(0)=0

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Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: To reduce the DE (x+2y-4)dx – (2x+y-5)dy=0 to a DE with homogeneous coefficients, use the…

A: See the solution.

Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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Q: %3D I+ ylz

A: Given differential equation is ddxyy'(y')2+1-(y')2+1=0                 (1) Since we know that…

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: Solve using Laplace transform y" – 6y' +13y=0, y(0)=0, y'(0)=-3

A: Using Laplace transform of derivatives

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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Q: Find dy/dx if y = x by using the Chain Rule with y as a compositionof y = 1 + (1/u) and u = 1/(x -…

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