Q2: (a): Solve (i) (x² D² – xD – 151I)y = 0 y(1) = 0.1, y'(1) = -4.5 (ii) 100 – 20 + d? N dN dt? dt

Q: a) Solve differential equation dx (y² – 4)(x – 1) = (x + 1): dy

A: Solution of the problem is given in the next step.

Q: Solve using separable differential equations dy X dx y2V1 + x

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Q: Find the particular solution to the differential equation d²y = 4e* + 3x² given y = -3 dx2 and = 3…

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Q: Solve using separable differential equations dy 1 dx y3

A: We have to solve using separating the variables. xdydx=1y3

Q: 4. Solve the homogeneous differential dy equation dx + 9xe x .

A:

Q: dy equation dx (6) Solve the Non-homogeneous differential x – y + 12 2т — 2у + 10 - -

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Q: Don’t skip any steps. Solve the separable differential equation : dy/dx = 3x^2y, y(0) = 2

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Q: solve the differential equation  a. dy/dx+9xy=x  x=0 and y=8 b. dy/dx+7x^6y=7x^6 x=0 y=5

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Q: d²y ) Solve the differential equation +y = dx² y'(0) = 0. sin(x) + cos(x) with y(0) = 1 and

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Q: Solve the differential equation by variation of parameters. 2y" - 4y' + 4y = e sec x y(x) = Need…

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Q: Solve the differential equation by variation of parameters. 4y" - 8y' + 8y %3D еx sec x y(x) =

A: The solution for the asked question is given as

Q: (D² + 4D + 5)y = 10 e-3*; when x = 0, y = 4, y' = 0.

A: GivenD2+4D+5y=10e-3x,y0=4,y'0=0.

Q: Using variation of parameters, solve the differential equation e y" – 4y' + 3y = 1+ ez' -

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Q: Eq (2) g (x)-2y(x ) =x (y (x l)

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Q: Find the general solution of the differential equation. (Use C for the constant of integration.)…

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Q: Solve the differential equation using Variation of Parameters et (D² – 2D + 1)y =

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Q: 5. x'dy-y'dx= xydy

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Q: Solve the differential equation below. (2xCosy+3x?y) dx+ (x³-x²Siny-y) dy=0

A: The solution is given as

Q: Solve the initial value separable differential equation (where a is a non-zero real number):…

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Q: x3 Show that y = is the solution for the differential equation dx dy = 2x2 -

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Q: Solve using linear differential equation (y+1)dx+(4x-y)dy=0, when x=4 and y=4

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Q: Solve differential equation dy/dx + y^2 = 2/x^2

A: Definition of differential equations helps to solve the given differential equation. An equation is…

Q: dy Solve the differential equation Inx 1-y' by variable separable method dx

A: We have to find solution

Q: Solve the differential equation by variation of parameters. 2y" - 4y' + 4y = e* sec x

A: The objective is to solve the differential equation by variation of parameters 2y''-4y'+4y=ex sec x

Q: (D² + 3D – 4)y = 18 e2×.

A: Complete solution of differential equation is :  Y = CF +PI

Q: Solve the differential equation 4y® ,6 dy 7xe-y' sin x? = 0 dx -

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Q: Solve the differential equation using linear coefficient  (5x+2y+1)dx + (2x+y+1)dy =0

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Q: Find the general solution of the differential equation. (Use C for the constant of integration).…

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Q: Q4: Solve the differential equation: 8- dx2 d²y 69 + y = 6. coshx dy dx

A: Some formulas: coshx=ex+e-x2 Given differential equation is: 8y''-6y'+y=6 coshx Auxiliary equation…

Q: By the method of change of constant, y"-2y'+y = e*/x X, %3D Solve the differential equation.

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Q: -X y" + 2y² + y = €²² ln x e^

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Q: Find the general solution of the differential equation y" - y – 12y = 30e2". Use C1, C2, C3, ... for…

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Q: dy Using linear first order differential equation, solve for the general solution of dx Please 2x…

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Q: Solve the differential equation - Xtan(y – x) = 1 dy dx

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Q: Q3)-(A) Solve the following simultaneous equations: dx 4t +x-y= cos(5) dt Int dx t -x +t == Int dt…

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Q: Solve the differential equation dy dx - =x + x – 3, if y = 0 when x = 2. 3 %3D

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Q: The second order differential equation for the instantaneous position s(t) for the vibrating mass is…

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Q: Q1) Solve a first order differential equation. dy -x + Vx² + y² dx y

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Q: Solve using separable differential equations dx 3xt? dt

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Q: Solve using separable differential equations dx 1 dt хet+2x

A: Using variable separabale method of differential equations.

Q: Solve using separable differential equations Vydx + (1+ x)dy = 0, when x = D 1, у %3D 4

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Q: 3.(i) Solve the Non-linear differential dy equation dx y = 4 • XVG 1- x2

A: Consider the provided question,

Q: Solve the differential equation using variation of parameters. y''-2y'+2y=e^x sec(x)

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Q: x dy -ydx -Vx²_yz dx =0

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Q: The order and degree of the differential equation 14()(음) + 12음()y= 16 dy dx - dz5 dx are

A: The given differential equation is:

Q: Solve the differential equation using inspection method d'y d³y = 24. dx5 dx³

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) = %D

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Q: :)dx + N(x, y)dy = 0 Y + x²- +

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.