5. Determine a solution of the following equation which satisfies the given condition: y-3y'+ 2y = 0 where y 0, y' 2, y"= 0 when x 0 1 %3D

Q: B(X-1)casy dy = 2x siny dx dif. den kleminin genel %3D Gôzümünü bulunua.

A: Given differential equation is: x-1cosydy=2xsinydx Rearrange the terms so that similar variables are…

Q: 2/3' 2/2, Suppose 3z? + 2y² + z² = 1 and z = g(x, y) > 0. Determine g, ) and gy 2/3' 2/2

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Q: Convert y " (f) + (1 – t) y' (t) + e¯' y (t) = t – 5t; y (0) =- 3; y' (0) = 4 into an in tegral…

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Q: Find the solution for following variable separable equation: x² (dx/dy) = y - xy , y(1)=1

A: The main objective is to solve the given variable separable equation.

Q: Q.4. Solve: y" – y' + y = Vxe*

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Q: Find a general solution of y'" = (- 50 – 50 i /3) y. ... y(x) = C, e +c2 e-

A: The given differential equation is y''=-50-50i3y Demoiver's theorem for fractional power  If rcos…

Q: 3. Find the solution of the following equation y'+4y= 0

A: This is Separable differential equation

Q: Q1. Find the derivatives of the following: 1. y = -x 2. s = 5t - 31s + 3 4x 3. у 3 4. w = 3z2 - 5. у…

A: Please find the detailed solution in below images

Q: 1. (x2 + y² + 1)dx + x(x-2y)dy = 0 (Non-exact Equation) Ans: x² - y² + xy - 1 = cx

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Q: (x2 – 1)y' + 2y = (x + 1)? |

A: We have to solve the differential equation. (x^2-1)y'+2y=(x+1)^2 (x-1)(x+1)y'+2y=(x+1)^2…

Q: S(y* - y-3)dy

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Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

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Q: x' = -3x + 2y, y' = -3x + 4y; x (0) = 0, y(0) = 2 %3D %3D

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Q: (0) = 2 is

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Q: y" + 6y' + 8y = 3e-2# + 2x

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Q: 2. yy = 4.x, y(1) = –3

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Q: Solve the following equations. 1. (x* +2y)dx – x dy = 0 2. y' = cscx - y cot x %3D 3. y' = x³ - 2xy…

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Q: Find y' and y". 1. x3 + y2 – 3x - y- 6 = 0

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Q: 5. Find general solution yu -Gy? +10y" = 0 %3D

A: Y(X) = c1+c2x+(A sinx+ B cosx) e3x Where c1,c2, A, B are constants.

Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1−x)y''+ (2x²− 1) y'+k (2x − 1) y=0…

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Q: Determine particular solution for y" – 4y' – 12y = 3e5. %3D

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Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: 5. (x + y)dy – (x – y)dx = 0. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find y' and y". 2. x² + y2 – xy +1 = 0

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Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: (1– 1)y' – y² +x²y+2x = 0, Y1 = -x² %3D

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Q: 7. Verify that y = x² – 1 is a solution of (y')4 + y? = - 1

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