Put the equation y x2 + 4x – 5 into the form y = (x – h)' + k: - |

Q: Find the solution of 2y-y² sec²(xy²) + (2x − 2xysec² (xy²))y' = 0 given y(1) = 2.

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Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

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Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

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Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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Q: Employ Picard's method to obtain y (0-1) of the equation y,=0 when x =0. :=x² +y}, given that %3D

A: Given IVP is dydx=x2+y2, y0=0 when x0=0 Let f(x,y)=x2+y2 , y0=0 when x0=0. Formula for Picard…

Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: dy-Hy-5 te %3D xp

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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Q: Find the general solution to y" – xy' = 0. -

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Q: Hw/ Find d if :☺ y =(x+2)*at @ y=X-1 at x=2 (2

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Q: Find a particular solution to y"+2y' + y =t

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Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: (2x+1)y' =e", with y(0)=0.

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: y" – 2y' + y = –3 – x + x²,

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Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: x²y" +xy' – 4y = 2x*

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Q: Give a particular solution for y" – 2y' + y = ex 1+x2

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Q: If y = (x + 1)(2x – Vx), then y' will be,

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Q: in yy = 2 y-x; %3D

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Q: solve for y in terms of t or x, as appropriate.

A: given: lny=-t+5 we have to solve for y in terms of t or x, as appropriate

Q: Solve for PS: y"+7y'-8y=0;x=0,y=0,y'=1 O y=9e^-t-9e^-4t O y=1/3e^-t-1/3e^8t Oy=3e^t-3e^2t O…

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: L,S, S yz tan xdxdzdy -1 J2y

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Q: The equation y3 = 3Bx is the general solution of 3y Oy Oy 3xy Ou' = 3y

A: We will form the differential equation using given solution

Q: Find the equation of a line perpendicular to 3x – 2y = 16 that passes through the point (9, 4). - Oy…

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Q: y" + 4y' + 13y = te-t %3D y(0) = 0 y'(0) = 2

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Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: y" + 2y" + y" = x + eX %3D

A: Given the differential equation y'''' + 2y''' + y'' = x + ex We find the particular solution form…

Q: y = v1 - x2 from a = 0 to r = ;

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Q: Obtain the general solution to the equation. dy y + 7x +1

A: Here we have to find general solution of differential equation

Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)>0    3t2…

Q: Differentiate the following implicit equation for y(x) with respect to r: 3x – a°y+ 4y³ = 6

A: Finding dy/dx

Q: What is diffential equation of y"-5y'+4 when y(0)=1 and y'(0)=1

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Q: If y = x*+2 then y' at x = 1 is equal to

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Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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Q: t²y" + 3ty' + y = 0, t> 0; y₁(t) = t-¹

A: t2y''+3ty'+y=0, t>0; y1(t)=t-1 lets use method of reduction of order to find the second solution.…

Q: If y = x(x – 1)* then y' at x = 2 is equal to

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Q: Find S- y dy Vy+2 using the substitution u +5=√√y+2.

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Q: Find the general solution of y"+25y=sec(5x)

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Q: "+y = sec³ x

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.