(3x2 − 2xy + 2) + (6y2 − x2 + 3)y′ = 0

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: (18x + 2y = 10 J 9x + y = 5 (x+4y 17 K (8x-7y 58) (9x-2y = 23) L (5x+y -2

A: As per our guidelines I am solving three parts J-L kindly resubmit other parts. J. 18x + 2y = 10…

Q: = [ 3u²-1 du u2 +1 (d) r(x) %3D 2x ch(z)

A: Add and subtract 1 in numerator

Q: Find the solution of 2y-y² sec²(xy²) + (2x − 2xysec² (xy²))y' = 0 given y(1) = 2.

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Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher-order linear differential…

Q: (3x"-1)(3) %3D 3 Y +1 e 3x"-1 s 3x"+xY =4 %3D -) m =4 30 that 3x +1 %3D 3x4+1

A: See the attachment

Q: x²y" – 2y = 0 %3D - x²y" + 3xy' -- 3 y = 0

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Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: y'(t) = In(y- 3) %3D

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Q: 2. x y-3xy = 4x + y+1 at (0, - 1)

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Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

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Q: How do I solve by elimination to find the solution of the two equations?

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Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: ① y" +16y=ex y-y-6y=2sin 3x ly-y-2y=3x+4 4y" +4y+y=3x² グッ 2

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: in yy = 2 y-x; %3D

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Q: (xi+axy-3)dk + 2x°dy -0 3)ck +2x²dy =0 Qxt -3x*y? +x = 3 +2xy -3n =0 O Option 3 O Option 1 x+ 6x…

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Q: -4x e Find a particular solution to y" + 8y' + 16y= x3

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Q: y''-3y+2y=5e^3x,y1=e^x

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Q: Find the first and second derivatives a) y=((4x^3)/3) -x +2e^x b)y=6x^2-10x-5x^-2

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Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

Q: 8.) (2y + 3xy - 2y + 6xjdx + x(x + 2y - 1)dy = 0

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Q: Find the general solution of 2y"+3y+y=3sin.x+xe"

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Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: 17. zdy + (x sec² () - y) da = 0

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Q: Find the general solution of the given DE 2xy^2 + 4 = 2(3-x^2y)y'

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Q: 2 1) x² + y² + 18x - 26y+246=0 CX+972+(₂-137² = 4

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: 18. (9x D² + 3xD + I)y = 0, y(1) = 1, y'(1) = 0

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Q: In x y of y = 3

A: Find your answer below

Q: 2x y'' – 3y' – 10y = 7e y(0) = 1, y'(0) = - 17 - %3D %3D

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Q: ( 1 - x2 )  y'' - 2xy' + 2y = 0   ;  y1 = x

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Q: (y – 2)dr - (x- y – 1)dy = 0 (coefficients linear in two variables)

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Q: 2) (r'y-2y kdx+ (y`x- 2x* \dy = 0

A: 2) Given that, x3y-2y4dx+y3x-2x4dy=0y3x-2x4dy=-x3y-2y4dxdydx=2y4-x3yy3x-2x4           ...(1)

Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: 3. 1 S [(2x - 4y)dydx 31 1 -1

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Q: 2. x³ydx+(3x4-y³ dy=0

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Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

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Q: Find the general solution of y"+25y=sec(5x)

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