Evaluate dx by completing the square. 2x2-4x+10 6. dy 5 +-y%D dx X Solve the first order linear differential equation Solve the first order homogeneous differential equation dy xy +3y dx x2

Q: 1 dx r2+6x+58

A: Integration problem......

Q: Solve the IVP: − 3x + 2y)dy = ( − 4x + 3y)dx where y(3) = 5 Solve your solution equation explicitly…

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Q: dy Find the solution of 2ху + dx X. 2у-1

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Q: Write each equation in the form M(x)dx + N(x)dy = 0 test for exactness and solve those equations…

A: The differential equation: M(x, y)dx+N(x, y)dy=0 is exact, if ∂M∂y=∂N∂x.

Q: dy (16) 2xy = x² + 2y² dx

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Q: d²y 2- dx -- 3y = 3e3x – 5e4x Solve - dx2

A: To solve the given ode.

Q: Solve the initial value problem. √y dx + (x-6)dy = 0, y(7) = 4

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Q: 1+x dx V1-x

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Q: 3. Solve the following initial value problem (3x² + y² + 2xy)dx + (3y² + x² + 2xy)dy = 0, y(1) = 1.

A: The given initial value problem is           3x2+y2+2xydx+3y2+x2+2xydy=0,      y(1)=1.

Q: dy Solve = dx Graph the solution. y(x) = = (y − 1)(y + 1) if the solution passes through the point…

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Q: image attached

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Q: 1 2 ху S S xe^ dx dy 0 -1

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: d²x 3. + 2x - x = 0, %3D dr (8x(0) = 1, x'(0) = 1; x(0) = , x'(0) = –1 %3D %3D %3D

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Q: How To Solve It? Which Method? dy/dx-dx/dy= x/y- y/x

A: ∫(1/y) dy  =log y +c ∫ (1/x)dx = log x +c  ∫  ydy  =(y2)/2   +c  ∫ xdx   = (x2)/2   +c log(a)+log (b…

Q: equation and general solution. 2. Solve the exact DE and give the general solution. c. (y' + kry -…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We have to find a linear differential operator that annihilates the given function 1+6e4x .

Q: (y* - 2xy)dx + 3x?dy = 0; when x = 2, y = 1

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Q: Question Calculate dx for w = ze(3²+2:). Do not include " de =" in your answer.

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Q: ODE

A: We use method of undetermined coefficient to find general solution.

Q: 17

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Q: 4.

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Q: e3x - 00 1+e3x –3 dx =

A: Given,            ∫-∞-3e3x1+e3xdx

Q: Write each equation in the form M(x)dx + N(x) dx = 0 test for exactness and solve those equations…

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Q: SOLVE FOR dy. x dx Yo WHEN x = 0; y₁ = 0; C = Constant C - Yo - x kyo

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Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: nd a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: y =(3+x)=¹/2, a = 1 Find the Linearization at a = a. L(x)=

A: To find the linearization of given function.