Solve the following differential equations 2d²y dx² d²y dy dx² dx dy 1) 2) 3) 4) 5) x² +4x +2y = 0, dx -5x +9y=0, y(1)=2,y'(1)=1 - d²y dy dx² dx - +12- +35y = sin(2x), d²y dy dx² dx d²y dy +6- dx² dx 5 +6y= 3x² − 2x+1, +9y=4exp(-3x), y(0)=3,y'(0) = 2

Q: The complementary function(C.F.) of the differential equation (D – 7)(D² + 7?)y = e7² is O (c2 Cos…

A: Solution: The objective is to find the complementary function of the given differential equation

Q: 4x +1 = cos y?

A: According to guidelines we should have been able to solve only one question at a time

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: The complementary function(C.F.) of the differential equation (D2 + 6D+ 18)y= z is_

A: In this question, we have find the complementary function for the differential equation.

Q: d²(x²+2xy+e» - 4) dxdy

A: Given To evaluate-4)d2(x2+2xy+ey)dxdy

Q: E.cos

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Q: -x-1 a) y' = +2yi-1 v(0)=1

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Q: (2yxe*+2x?ye*)dx +(6y®x -2x²e*)dy = 0 1 (x, y) a) .2 xy² Show that the differential equation is…

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Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: 5) (4xy + y) dx - 2 (x°- y) dy = 0 1

A:

Q: ху — 1 dx x²y 1 xy2 dy = 0

A:

Q: 2) (3x²y+ 4e)dx + (x³ + 4xe + 2y)dy

A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: Solve the Cauchy-Euler differential equation d'y dy +2x-20y xr + 2x +1 dx dx

A:

Q: If (2xy?+4) dx +2 (x*y-3) dy = 0 then ƏP/ay # ƏQ/ax *

A: Given: The equation is, 2xy2+4dx+2x2y-3dy=0 And ∂P∂y≠∂Q∂x To find: Whether it is true or false.…

Q: Determine the general solution: (dx/dt)A3 - (dx/dt)^2 - 4x = 0 Select the correct response: O y= c1…

A: Topic:- differential equations

Q: find general Solution of DE. 4xg dx +x'dy +3y°dx +2xydyexd

A: The objective is to find the general solution of differential equation 4xydx+x2dy+3y2dx+2xydy-xdx=0

Q: Use the exact techniques to determine the solution to (2y? + 2y + 4x2)dr + (2ry + x)dy = 0.

A:

Q: (х + 2у)dx - Зydy %3D0 o x* - 6x²y? + 8xy – 3y* = c o 3x* - 8x*y? + 6xy - y* = c o x* + 3x²y² – 4xy³…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: y²dx + (3xy + y² − 1)dy = 0 ex + Iny + dx + ( + Inx+ siny) dy = 0 2)

A: (a)

Q: Find dy/dx if y=- O dy dx Ody dx O dy dx O dy dx = = = 1-t 1+t = sec 2t (1+t) ² (1+1) 2 sin2t cos2t…

A: To find dydx if y=1-t1+t and  x=cos2t.

Q: 1) d कर dy + 4x3 + 2y = 0,

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Q: 꾸dz + Pdy =0, y(-1) %3D2. (3-y) dx + (y 2x) ry²

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Q: d²y dx² + 12 +35y = sin(2x), dy dx

A: Given differential equation:- d2ydx2+12dydx+35y=sin2x

Q: dy 1. dx = 6y d y 36у dx2 dy = -36y dx2 2. 3.

A: We are entitled to solve only one question at a time and up to 3 sub-parts only. So, we will answer…

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: d'y Find dx2 (a) y = 6x3 – 7x² + x dy dx? (b) у — 7а? — 6х +9 - d²y dx? x + 2 (с) у — d'y dx2 (d) y…

A: We will solve the problem

Q: 3) y sin-ly² dy

A: