(2x – 3y)dx – (-6y + 4x + 1 )dy = 0

Q: /3 2 %3D

A: To find: The value of dydx. Given: The equation is y=x35x2+1-23. Formula used: Chain rule of…

Q: dy-3x²e-3x dx = 3y dx

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Q: dy 2x + 1 y(-2) = -1. dx 2y

A: To solve the IVP: dydx=2x+12y, where y-2=-1. Solution: Separating the variables of the given…

Q: ● √3x dy dx √x² + y² So So

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Q: (2x – 5 y dx + (- 5.x + 3y² kdy = 0||

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Q: (х- 4y - 3) dx -(х-бу— 5) dy %3D о ans. (x - 2y - 1)? %3D с (х-Зу- 2)

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Q: 4. y(2x2- 2x - y)dx + xy dy = 0

A: We will solve the problem

Q: 7. 5d'y. dx dx -6x , y(0) =0, y(0)=-10

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: x-y 2 dx dy wer (2x-u)

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Q: (y-4x-1) dx= dy %3D

A: (6) Given differential equation is y−4x−12dx=dy....1 We have to find the solution of the given…

Q: 2. (2x +y -3) dy = (x + 2y -3) dx.

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Q: x² x dy +y=- 3 dx 3.

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Q: 2.) 2 (x -y)dx + (3x² - GxY - 2x) dy

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Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: 2. (6x2 - y+3)dx+ (3y2 – x- 2)dy =0

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Q: y(3x-2)dx +x (1-2 y)dy=D

A: We will solve the problem

Q: Find the solution. 2y dx = (x2-1)(dx - dy) %3D

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Q: dx 1. dy y 3x :-5x2 dy 2y 2. dx = -4x²

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Q: x² - 3 y : х +2 dy dx

A: Given: The function is  y=x2-3x+2   To determine: dydx of the function y=x2-3x+2

Q: dy -x-ly=²sin2x dx || 2 . 2号=2でッる xp

A: First order differential equation of the type, dydx+Pxy=Qx can be solved as follow: 1. Find…

Q: y = (ax-1) (6x.+5]%3 find dy dx 10

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Q: (6xy-y") dx+ (4y +3x - 3y*) dy = 0 (a)

A: Given:-(a) 6xy-y3dx+4y+3x2-3xy2dy=0

Q: (구+w)@-2y' -0. – 2y² = 0. x +xy %3D dx

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

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Q: 3x + 2y dy 30. dx y(-1) = -1 3x + 2y + 2

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Q: (3x - y +6) dx + (6x – 2y - 6) dy = 0 Answer: 7x + 14y + 18 In ( 21x - 7y-12) = C. %3D |

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Q: (x-3y+4)dx + 2(x-y-2)dy = 0

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Q: dy 2x – y 21 dx x - 2y

A: The given differential equation isdydx=2x-yx-2y

Q: (6x -3y +2)dx - (2x– y – 1)dy = 0 (coefficients linear in two variables)

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Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: y = (3x² + x-2)-1; 49 -1 , dy dx

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Q: dy e2x -3 Find if y = In %3D dx 1-4x

A: SOLUTION-

Q: x/1-y2 B, dx %3D 1+x²

A: dydx=x1-y21+x2

Q: (бху — у')dx + (4у + 3x* - Зху")dy %3D 0

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Q: (2x - y)dx(x + 4y)dy = 0

A: As per the rules, we can answer only the first question and other can be reposted.

Q: dy y2-8y+5 13-1 dx x2+2x+5

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Q: 3. ( 2x-y+ 2) dy + (x- 2y+4) dx =0

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Q: 1. (x- 4y- 3)dx - (x – 6y - 5)dy = 0

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Q: 2 y (y² - 3x² ) dx + x (3y²-x²) dy = 0

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Q: %3D 4x3 dx 2. х3dy + 3x?y dx 3. х3 dy + (3x?у — хе*) dx %3D 0 -

A: These are the first order and first degree DE. Solutions are given below:

Q: 1. ху' %3D у + уx? — у? d²y 2. х- dx² = 2-a dy dx 3. Зуу'у" — у'3 +1%3D0

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Q: d²y dy 3- 4y = 3e¬* dx x- - dx2 -

A: Given differential equation is

Q: dy dx 1. dy 2- dx=2xseey 3-(1-x) 2y

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Q: (9xy-2y2) dx - (6x²- xy) dy =0

A: 9xy-2y2dx-6x2-xydy=0dydx=6x2-xy9xy-2y2dydx=x6x-yy9x-2y

Q: dy 3e-2x %3D dx 3. (x2 + 5)dх — (2у — 1)dу %3D0 (2у — 1)dy 30 |

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Q: (y - 2x - 9) dy = (x + 2y + 7) dx

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Q: 3x²y dx (x³ + y³)dy = 0, y(1) = y(1) = -2 -

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Q: d³y d²y +6 dx3 dx² dy -+ + 11 ax+6y = ex + cosx dx

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Q: dy 5 - 5y =-ラ*y xy³ dx

A: The given equation is a Bernoulli's equation which is a special type of first order non-linear…

Q: (3x'y +)dx + (2x'y-1)dy o

A:

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.