31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

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Q: The particular solution of y(x+y)dx + (x +2y- 1)dy=0; y(0) = 2 by NEDE is

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Q: Solve: ()* +1 y In z 6x In a+ 2x = 9y + 36y + 18 In y + C O 6x* In z – 2x = 9y? + 36y + 18 In y+ C O…

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Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Find the particular solution of y2dx+x(x+y)dy=0, when x=1, y=1. Let x=vy.

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Q: 4. xydx + (y √ x² + y²-x²) dy=0

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Q: A particular solution of 4x² dy dx dy 4 is vx +8.x- +y = de

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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: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: 1.Solve the given problem W = f(x, y, z) = 3x²y+ yz² + 2z³ fxis equal to ? fyis equal to ? fzis…

A: Follow next step

Q: If y = x3 – 2x2 + 3 and x = t² + 2 find dy at t=2. dt %3D

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Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: 7. Show that y(t) = c,e¬# +czte¬2# is a solution to y" +4y/ +4y = 0. Determine the constants c and…

A: The given equation is y"+4y'+4y=0. A second order linear, homogeneous ordinary differntial…

Q: Find the solution of the following 3(1 + t ^ 2) * (dy)/(dt) = 2ty * (y ^ 3 - 1)

A: The solution to the given differential equation is explained below.

Q: 41n <ys 28 31r x = sec* (7t) – 1dt, | 21 41x 28

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Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: Find a particular solution to y"+2y' + y =t

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Q: Find the general solution of (x^2+x)dy=3dx

A: Given difeerential equation, (x2+x)dy=3dx

Q: I Find a particular solution to y" + 4y' + 3y = 3te*. %3D Yp =

A: Solution:-

Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: Find the particular solution of y²dx + x(x+y) dy=0., when x=1, y=1. Let x=vy

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Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

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Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: 1. The complementary equation to dt² + dy + 4y = 5e-³t is:

A: Solution is here

Q: What is P-(y) if the given DE is xydx – (3y – x²)dy = 0? -2y 2y 2 y -2y-1

A: Given : Linear differential equation  Need re write in x form as follows dx/dy +P(y)x=Q(y)

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: We wish to find the solution to dy = 26y that passes through the point (x, y) = (1, 3).

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Q: Show that the homogenous equation (Ax + By) ⅆx + (Cx + Dy) ⅆy = 0 Is exact if and only if B = C.…

A: Please refer the attached image for complete solution.

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: d²y + 9y = 2 cos(3x); y(0) = 0; y'(0) = %3D dx² 3

A: Given differential equation is The associated auxiliary equation is Complementary function of…

Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

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Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

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Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

Q: u = 4x2-x+8  and y = u4 Find dy/du

A: