1. Separating the variables dy 1 x(y- 3) =D4y dx %3D

Q: II. Bernoulli's equation: dy 4. dx -2y %3D글x" xy3

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

Q: dy x +1 xy %3D dx

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Q: Express the relationship between a small change in x and the corresponding change in y in the form…

A: Consider the given function

Q: (x-2) (x³-4) Vx² +1 dy 1. If y = then equals to : dx

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: 2. dy _ y² – x² dx Ty 3. dy_ y(x + y) dx dy x² + xy + y² dx 5. dy Y +2, dx 4.

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Q: d'y ,dy dy dx 2 2- 24e* + 40e S* dz dx +

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Q: d*y Obtain a particular solution for dx+ d²y *+y = x3 + 2x + 1 dx² dx + +

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Q: 1 6. If y = 2x + 1 d'y, what is dx? d'y d'y В. 8 4 - 6 A. dx 2 (2x + 1) С. dx D. dx dx 2 (2x + 1)…

A: NOTE: According to Bartleby's guidelines we can only do one question at a time. So i am doing Q6.…

Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

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Q: So SAF+1° y¹/3 x7 +1 (Hint: Change the order of integration to dy dx.) Y dx dy.

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Q: Bernoulli dy + xy = dx y # 0 уз

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

Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: Find dy/dx and d2y/dx2 without eliminating the parameter. x=1-t^(2), y=1+t

A: x=1-t2,  y=1+t Differentiating with respect to t, we get dxdt=0-2t  &  dydt=0+1⇒dxdt=-2t  &…

Q: 1 1 d y dy 2 3 X - х —- %D dx dx

A: Topic = Differential equation

Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: 5 If y = dy then dx %3D x+1

A: Given that: y=xx+15

Q: The integrating factor of dx dy 2 y= 3x² is а. b. 1 x С. d. 1

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Q: dy - Solve + 3y + 2. y dx = x, given y (0) = 1. %3D dx

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Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: 2 cX S* (x – 2y + 3) dy dx 0.

A: We have to find the value of the double integral ∫02∫0x x-2y+3 dy dx At first we take integral with…

Q: S S* e*(y + 2z) dz dy dx

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Q: dy dy dx +3. + 2y = 0, subject to y(0) = 2 and y'(0) = –6 dx2

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Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: dy 1- dx e-x-y-2 У (0)- -2 dy 2- dx ylny y(0)=e? 1+x2

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Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

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Q: 1 d'y dy + 5y = 0, subject to y(0) = 0 and y'(0) = 40 dx 4 dx2

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Q: 23. dx + 4y = 0; y = cje2 + czxe2x dx d'y + 2x - x + y = 12x²; dy 24. x dx dx "dx y = cx- + czx +…

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Q: dy dzy If y = e2x –2e¬3x, Find at x = 1 dx 'dx2'

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Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

Q: General solution of (ylny − e¯xy)dx + (² + xlny) dy = 0

A: Let's solve given diffrential equation.

Q: Solve for the DE: (3x²y - y)dx + (x³-x+2y) dy =0 ; y(0)=2

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Q: d*y dy is dx x dx ferential

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Q: dy 1 a) dx dy y=3+e dx 4

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from x = 0 to x = 2

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Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

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

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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: b. (xy - y)dx + (x² – 2x + 3y)dy = 0; when x = 1, y = 1

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Q: 1 -dy dx = 0 dy 2.xy- + y? – 2x = 0 | d.x

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Q: Find the solution y=y(x) of dy +y dx subject to y(1) = 1.

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Q: 26. (a) J. Jo dz dy dx ~2 r2-y (2-x-y (b) dz dx dy -2 p4-y² dx dz dy (c) -2 Jo

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Q: Find the general solution for dy dy +2 + 4y = dr dx? e2= (1+ x²)

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

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

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Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: 6. - ydx + (x ++ Jy )dy = 0 7. (1+x*)dy + x(1+ 4y°)dx =0 8. (e* + y)dx + ( 2+ x+ ye" )dy =0 2y 9. 4.…

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Q: 1. dx + 2y = e^* dx 2. dx dy + 4 + 4y = 5ex dx d'y 3. dx + 4 dx + 3y = cos 3x

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Q: find 12. (x + y + z) dy dx dz –y² ¢2x+y 13. dz dy dx 14. V4-y²• kp xp zp -2-x-y •1 cl-x c4-x²-y 16.…

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Q: 3X-Y-4) dy wheh X=4 i y=l ty dx

A: You can solve by any method

Q: d*y d²y dy .3 Obtain a particular solution for dx4 + + y = x³ + 2x + 1 dx dx2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.