D xy4dx +(y+1)E? dy =

Q: d'y & dx Find d'x to the : dy *yーy=7 %3D7

A: We have the expression x2y2-y=7. Differentiating both sides of this equation with respect to x, we…

Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

Q: x dy +y dx exyfdx 36

A:

Q: d'y dr2 dy - 2 +y=3 e4x, given y(0) dx 1 and y'(0) =4; 3.

A:

Q: dy + y = x dx 4.

A: Given: dydx-y=xey

Q: dy 4. a2+ y? = ry (Bernoulli DE) dx

A: Answer and explanation is given below..

Q: Q2: If y=t? and x=3t-1 find dy/dx

A: y=t2, x=3t-1Formuladduun= n un-1

Q: Find dy/dx If y ex A 2/א"e ],/איe D-2V B.

A: We have to find dy/dx.

Q: dy If y = (t + 7t + 6) (4t² + 5), find dt

A:

Q: If y=x^2 e^2x then dy/dx is equal to

A: we have,y=x2e2xdifferentiating both the sides w.r.t. xusing product rule,we…

Q: Find the solution of dy 2x- +y =x is dx

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Q: Obtain the general solution. d²y e* 1. dx? dy 2 +y= dx x² +1

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Q: If y = t“, then dy 4t³. dt

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Q: if y = (3x? + 4x – 7*)e, then dy/dx is:

A:

Q: dy dæ 2 and dt at x = 3 if y = 3x? 4. Find dt

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Q: (e* + y)dx + ( 2+x+ ye )dy =0

A: See the details solution in below

Q: : x d²y dy dx² dx + +my = 0, given that

A:

Q: 36. dy dx y=x2/3

A: The given integral is ∫01∫x231xey4dy dx. From the above integral, the region is given by…

Q: f) e*dx-y'dy = 0

A: As per guideline we have to solve one question

Q: SíS(x² + y²) dx dy 0.

A: To evaluate the given iterated integral.

Q: Show that y=xe-x satisfies the equation dy/dx +y=e-x

A: We find dy/dx using product rule

Q: Calculate (ay² + y) dy dæ. 3.

A: We use the properties of integrals to evaluate the given integral.

Q: x³ex? (Xie, 2010) y In y dy 2. dx

A: Given query is to find the solution of the differential equation using seperation variable.

Q: calculate  d^2y/dx^2 for y=e^7-2x + 12

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Q: dx 2x dy y 3.

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Q: dy d. dx = y(xy3 – 1)

A:

Q: In(y) dy V. 6.

A: This is a problem related to integral by parts. Based on the general formula of integral by parts we…

Q: d² dy +5 dy + 5y = e-t sint, where y(0) = 0 and y' (0) = 1.

A: Given: The equation is d2ydt2+5dydt+5y=e-tsint. The given initial condition is y0=0 and y'0=1. To…

Q: dy 2 + y = 0, y(0) = -3 dt

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

Q: dy 4. dt + 2, y(1) = 3 t

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Q: dx y In y || 2.

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Q: d ef dt (F(=") = %3D dz dz 13

A: We have to find

Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: (e* + y)dx + (2 + x + ye')dy = 0

A:

Q: dy 4. y = e*y? dx

A: Solution 4: Given differential equation is dydx-y=exy2 We can write it as 1y2dydx-1y=ex         (1)

Q: d V3i dt = dx x²

A:

Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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Q: x dx dy _dy V4 +

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Q: dy 1- J ++y2

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Q: Find the solution of the D.E. below: 2(2x + y)dx – xydy = 0

A: If a function f(x,y), satisfy the condition f(kx,ky)=knf(x,y), then it is called a homogenous…

Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: If y = In dy then dx 10 10 20 et - E) eT – 10 A) x – B) eT D) 0 eT – 10 10 — еT Of –

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Q: S| (x? + y²) dx dy 'D Where D: x2 + y² x²

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Q: Find d²y/dx² for the following equations: e) xy + y² = 1

A: Given equation is xy+y2=1 find d2ydx2

Q: M                   dy/dx - y = e^x y^2

A:

Q: (e* + y)dx + ( 2+ x + ye )dy =0

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Q: Find dy. 37) y = 5~x +Z

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Q: Find d²y/dx² for the following equations: e) xy +y2 = 1

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Q: Obtain the general solution to the equation. dx 8 y: + 4x = 9y dy

A: