Find the series solution of (4 – x²)y"(x)+ 2y(x) = 0 about xo 1 %3D %3D

Q: 는 (1-5)~ dx =C 1+2e dy + 2 Find the gereral solution.

A: To solve the differential equation:  1+2eyxdy+2eyx1−yxdx=01+2eyxdy=−2eyx1−yxdx⇒dydx=2eyx−1+yx1+2eyx

Q: Show that 1/2 ( Tn + Mn ) = T 2n

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Q: Find the series solution of the equation, near x = 0: d²y d.x² - dy dx x + y = 0.

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Q: n of (3x²–

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: 1. and X = 2. %3D Find at t =2

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Q: In (T-(Tin+ (pvc)) To-(Tin+()) + t (V) = 0

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Q: Q2. (a) dy = (x + y + 3)² (b) 2xy4 = 4x² + 3y?

A: Given that a)dydx=x+y+32 b)2xydydx=4x2+3y2

Q: on f(x, y) = 3x + 9y subject to th %3D

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Q: y′=(3t2+4t+2)/2(y−1),y(0)=0

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Q: Solve the ODE by the Euler method: given 2y" = -4y' - 1.5y y(0) = 3 and y'(0) = −2.5 with step h =…

A: To find- Solve the ODE by the Euler method: 2y'' = -4y' - 1.5y       giveny0 = 3 and y'0 = -2.5with…

Q: dy = VE+y-1 de

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Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

Q: 3. Find the correct form of x(s) and stop. State x(s) as a single fraction. x" +7x' + 6x = 2t x(0) =…

A: Explanation of the answer is as follows

Q: d²y dy (1 – x²). + 2x + 5(5 + 1)y = 0 | - dx2 dx

A: The given Legendre equation is of the form pxd2ydx2+qxdydx+rxy=0. Let yx=∑n=0∞anxn be the power…

Q: 2xydy + (y- 3x-)dx = 0;y(3) = 2 O xy² - x³ = c O x³ 2 – xy² = -15 Ox* - xy? = 15 O x³- xy? = c

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Q: 3:30 A3. If y = e2x+5 then y' = %3D LA) 2e2x+5 (b) e2x+5 (c) 5e2x+5 (d) e2

A: Given query is to find the derivative of the expression.

Q: Q2: Apply Taylor's series method to solve = 2x -3y, y(1) = 2 and use it find the value of dx y(1.5).

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Q: Find Y(s) in the form p(s) SIMPLIFY COMPLETELY. 9(s) * y" – 9y = e³t y(0) = 1 y'(0) = -1 %D

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Q: Solve dy = ex-y+x²ey dx

A: In this question, we need to solve this problem.

Q: Solve this equation using a power series

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Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

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Q: y'

A: The function is given as : y'''-y''-2y'=0. To find the general solution of the function , The…

Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

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Q: 6. xydx + 2(x² + 2y²)dy = 0 ; where x = 0, y =1

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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: For the difference equation given by y(k + 1) + y(k) = 3 (1/2)k with y(0) = 1 %3D Find the…

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Q: 2y(x? — у + х)dx + (x? — 2у)dy %3D0

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Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: tind the particular solution of the differential (0?+ 4D +3)x given that t- 0, and dx -2 %3D

A: Given differential equation is : D2+4D+3x=e-3t At t=0, x=12 Att=0 ,dxdt=-2

Q: Find a family of solutions for x2y dx +(x2-x)dy=0. Assume x>0

A: Given differential equation is: x2y dx + (x2-x) dy=0x2y dx=(-x2+x) dy This given differential…

Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…

Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.