dy d'y and Find dx dx2 x = t? + 2, y = t?+ 9t (i) 1+ (x- 2) dy %3D 1+(x- 2)() dx 3 d²y -{(x-2) %3D II

Q: (2x + 3y - 1) dx - 4 ( x + 1) dy = 0

A: Explained below

Q: dy 3. + + 2y + y² = 0,yı = -2 dx

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Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

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Q: dy 3 1 +-y = 27y3 Inx, x > 0 dx

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Q: dy y- dx2 dy dy = 7(y+1) dx? dx

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Q: Homogenous (2x²y + y³)dx + (xy?. 2 – 2x³)dy = 0 -

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Q: 67. = 2x − 7, y(2) = 0 dy dx dy 68. = 10 - x, y(0) = -1 dx 1 69. dx + x, x > 0; y(2) = 1

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

Q: dy + (3y - ex) dx = 0

A: Given differential equation is  x dy + (3y - ex) dx=0

Q: dy| 2х — 6 - Find- , where y = dx\x=1 x + 2 Enter the exact answer. dy dx=1

A: Solve

Q: 2ydx-(1-x^2)dy=(x^2-1)dx when x=0 and y=-1

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Q: (x²-xy-y²\ (x2-ху-у?) dy = 0 dx + r2-v3

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Q: dy Q2 Find dx of x = *-Y 2 x+y

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Q: 1) dy_4x+2x°+2 dx y+1 2) dy-x+3y dx 2х

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Q: = 6 + 3t, y = −8t;  dy dx

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Q: x*y' = x* -y*

A: Differentiation of implicit function

Q: dx 7. Inx- dy y 8. Vx2 +1 dy + Vy² – 1 dx = 0.

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Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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Q: 2. ( 3 x - 3 y - 2) dx - (x - y + 1) dy = 0

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Q: sin(x + y) dx (3x − 2y + 1) dx + (3x - 2y + 3) dy = 0

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Q: (3-y)dx + (y-2=) dy = 0, y(-1) = 2. ry2

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx Зdу — 4xу dx

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Q: dy 21+ dr2 (vii) dy\2] & (dy\- da2 \dx². (viii) = 0. (ix) () z\ip, + 5y3 = x. dx.

A: (vii) The equation given is d2ydx2=21+dydx232. Squaring both sides. d2ydx22=41+dydx23 Order = 2…

Q: 2. S dx exte-x 3. fx sec² x dx 4. esinx cos x dx

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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: solve x (dy/dx)=x^2y^3 - y, y(1)=1

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Q: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: dy/dx=4x^6sqrty,y>0

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

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Q: dy dx = (1 + y²)ex dx

A: As per the instruction, we will be answering the first question. For (1),      y'…

Q: dy tanx for y = dx 1-secx 1) dy (1-secx)sec x+secxtan2x dx (1-secx) 2) dy (1-s8cx)secx-secxtan²x I3I

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Q: Find the function y(x) satisfying =4 dy =4x-3 and y(6)30. dx The function y(x) satisfying --4x-3 and…

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Q: dy 2. dx = x³(y – x)² +, Y1 = x,x > 0 y У1 — х, х > 0 dy 3. + 2y + y² = 0,yı = -2 - dx

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 1) x(2y-3)dx +(x'+1)dy-0 (x+1)(2y-3)=c ans:

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Q: 32. (2x-y+4) dx + (x-2y-2) dy = 0

A: Consider the differential equation(2x-y+4) dx+(x-2y-2) dy=0. The objective is to solve the…

Q: dy 2 = 3, ,3 X'y' - xy dx

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Q: 2x-1 11. y = 5x+2 12. y=(5x² + 2x + 1 )3 13. y = V2x + 6 /14. y = 15. x = 2x + 3, what is dy/dx? =…

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Q: dy of x = *-y 2 dx Find x+y

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Q: dy Зx+2у-5 %3D dx 2х+у-3

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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: 18) fvī dx 19) f se'de 3e dx 20) (3x - V5x + 2) dx

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

Q: 2x - y + 5) dx - (2x + y) dy = 0 where x= 3, y=7

A: Let's find.

Q: dy 3 - dx2 4 y = 1/2 dy/dx = -1 when x = 1

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Q: dy Find dx by implicit differentiation. 3 +y = 25 -1 dy 9x а. dx 4y dy b. dx 4x Зу -1 dy 4х с. dx 1…

A: We need to find dydx of x23+y32=25. So,                 x23+y32=25Differentiating both sides wrt…

Q: dy Зx+2у-5 dx 2х+у-3

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Q: d²y dx dy – 3x- dx ential equation x².

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Q: Solve dy 2-x -subjectto y(1) = 0 dx ху

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