( 3u + 3uv – 4)dv + (v+1)*du =0

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

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Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of dy -2y + x2 + 2x = 0 dx…

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Q: 4. (15pts) Identify (write down) the type of DE, and find the general solution. (y – 3x)dy = (x +…

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Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: Q6: Determine a particular solution of the equation d'y +4y 4x cos 2x dx Using D-operator method

A: The solution is given as

Q: 1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

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Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

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Q: b) Use the initial condition x(0) = 2 to find the particular solution of dx - 2x = 2e3t dt

A: We have to solve the given initial value problem  As per the answering guidelines we need to answer…

Q: Find the general solution of the DE y’’ = xsin(x)

A: Topic = Differential equation

Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

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Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

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Q: dy -y2+1,ysCJse Cantial cokditian.

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Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

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Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

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: solve the DE:   (2y^3-x^3)dx+3xy^2dy=0 ; y(1)=1 using 3 methods.

A: Let's find.

Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: 2 2х-4 2у — 1 dydx x + 1 ) Q2. Evaluate the double integral

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Q: 4. Obtain the general solution of x? y dy dx

A: By Bartleby policy I have to solve only first one as these are all unrelated problems

Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: 3X 7- (0²1)y=K²" yp-e (4X-3} 8-(0-20+4)y=x+3x-5x+2 yp=Dx yo= 3.2 -2K 2. to-(D²+2}y=x²+xre+cos3X éte…

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Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of -2y+x² + 2x* = 0 %3D dx

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Q: Solve the disfertial equation xy' -Y =Xtan ) %3D

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Q: Example 5: dy Find the particular solution of, y(1+x²)÷= 2x(1 – у?); y(0) = 0 dx

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 1 c2(1-z) Evaluate Sa-2) s(1-;-2) dy dx dz

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Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: -dt solves the initial value problem 35. Show that y = x² + d² y 2 x²* 3; y'(1) = 3, y(1) = 1. dx…

A: Given

Q: -2 2 dx dt -12 8 with the initial value -2 x(0) = -5 x(t) =

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Q: II (2x + 3y + 4:") dV , where B = {(x, y, 2) | 0 < x < 1, 0 <y< 2, 0< 2< 3}

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Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

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Q: -18 21 dx dt -14 17 with the initial value 10 æ(0) =

A: Given that ; dxdt=-1821-1417x with the initial value. x0=105

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: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

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Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

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Q: 4. Find dy and Ay for y = 3VT-1+2x at r = 2 with dr = Ar = 0.2. %3D

A: The given equation is y=3x-1+2x. Given that x=2, dx=△x=0.2. Now,…

Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

Q: olve the initial value problem by standard method  (x^2+3y^2)dx-2xydy=0,  y(2)=6

A: We need to solve differential equationx2+3y2dx-2xydy=02xydy=x2+3y2dxdydx=x2+3y22xy