Solve by power series x y" + (1– x) y' –y = 0, X>0 %3D Find a general solution for the following system. Show the details of your worh y--y,-sin(t)= 0 y-4y,-y, = 0 |

Q: y" + y = sin x %3D

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Q: Find the solution. y'+=V5.y(1) = 0

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Q: y' = (1-x)y²+(2x-1)y-x a special solution of the equation y1(x)=1, Find the general solution of the…

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Q: (x-2)(dy/dx) – y =(x-2)3 solve homogenous equation by linear equation method

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Q: Find the general solution of y + (1/3)y = e"y Show your solutions on a separate sheet of paper. A…

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Q: – 2y' = 2t 2x – x + y' – 2y = 7 x" + x

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Q: 4. Šolve Člairaut equation y = xy' – 2In(y' +1)

A: The given clairuat equation y=xy'-2lny'+1 s the first order nonlinear ordinary differential…

Q: x' = (C )x ´sec X + 0, 1

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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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: x3y" – 5xy' + 9y = 0 -3x y" + 5y' + 4y = 10e %3D

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Q: 6z dy (78)a

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Q: Solve: у" + 5у'" — 2y' - 24у — 42е 5t 2y' — 24у 3D 42e — 2, у'(0) — — 6, у'"(0) —D — 30 | | | y(t) =

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Q: y' =xy

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Q: Find y' and y". y' y" = y = (²+ √x)³ 3

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Q: Solve: y''' – 3y'" – 6y' + 8y = 0 %3D y(0) = – 6, y'(0) = - 12, y'"(0) : - 54 %3D y(t) =

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Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: 3 (x-2) y'= y + 2(x-2)

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Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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Q: x’y" – 3xy' +3 y=3 ln x- 4 y(1)= 0 y'(1) = 1

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Q: Solve the following IVP y" - 10y' +9y = 5t, y (0) = -1 y' (0) = 2

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Q: (x+1)3 solve for y'. %3D x2

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Q: 3. (2x – y)3 = 3x?y, find y' %3D

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Q: Find a particular solution to y"+3y'+2 y = x² - 3.

A: Given that,         y"+3y'+2y=x2-3  ⇒D2y+3Dy+2y=x2-3 Where, D=dydx ⇒D2+3D+2y=x2-3  Let, FD=D2+3D+2…

Q: (D-1)x -8y = e :+(D+1)y = te'

A: Let us consider the given system of the differential equation then to solve the system of the…

Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: Show that u(x, y) = y²e* + 3x² is the solution for u = yuyy + 6x . 2

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Q: y' = 5y + e-2*y¬2

A: The differential equation is given as , y'=5y+e-2xy-2 find the solution.

Q: у 7. y' +²√y = 0, y(1) = 0 - x

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Q: y'-2 xy=2 y (0)=1

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Q: * If y" = 9x – 6x² ,y'(2) = 4, y(2) = 12 ,find y %3D

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Q: Solve 2y-y² sec²(xy²) + (2x−2xysec² (xy²)) y'= 0; y(1) = 2

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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.