Determine the r- and y-intercepts for h(x) = 6x – 42. Solve -7x – 8y = 1 for y.

Q: Q6. Find the general solution using variation of parameters of y"+ 4y 8tant %3D | 2

A: To solve the differential equation:

Q: solve using the appropriate method. (y − 1)y'= t , y(1) = −3

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Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

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Q: Solve using variation of parameters (D^2 − 1)y = e^x + 1. answer: y = (c1 + c2x)e^3x

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Q: solve for y in terms of t or x, as appropriate ln y = 2t + 4

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Q: ) Determine the Cartesian Equation perpendicular to the line L1: 4t – 2y = 8, -3t = 6 – 2x with a…

A: Write L1 in Cartesian form. Then find its slope or gradient then use it to find the slope of the…

Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

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Q: y'-5y=x'e* – xe³* - хе

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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: Q2/ A/ Find the equation of straight line passing through the point (1, 2) and parallel to the line…

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Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

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Q: Find the perpendicular equation for y= − 1/8x+8 with the x intercept at x=-8. Answer in y=mx+b form.

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Q: (a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following:…

A: (a) The solution curve with the direction field that satisfies the initial solution y0=0 is as…

Q: Q. Solve the equation using Variation of Parameters: y" – 5y' + 4y = x. -

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Q: Find all values of r for which the function y = e^(rx) satisfies the equation y'' + 5y'-6y=0

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

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Q: Q2: solve the equation dx 2x dy y y 3.

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Q: Find the values of r for which y = e"* satisfies the equation y +2y -8y=0

A: The given differential equation is: y''+2y'-8y=0

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

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Q: y=3+2x– x² and | about the y-axis.

A: Given:

Q: G) (2x-yJdx + (4x. +y-3)dy=

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Q: Write the equation of the line tangent to the graph of y? 2y + 10x 17 at (2, – 3). - The equation is…

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Q: Q5. Check whether the following statement is true or false. d²y + y? = 0 is non- linear equation.…

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Q: Solve for the solution for the equation: y' + xy = 6x/y with the condition of y(3) = 6.

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Q: With y(5) = 0, solve y′ = e−y(2x − 4)(show all steps)

A: This question can be solved by variable separable method. In variable separable method, separate the…

Q: Use an appropriate substitution to solve the equation xy' + y = -2xy², and find the solution that…

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Q: Q1: using variation of parameters to solve: * y"' – 2y" – 21y' – 18y = 3 + 4e-t %3D

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Q: Find the x-intercept of the line by substituting 0 in for y and solving for x -4x -6y=36

A: For x intercept we put y=0 in given equation

Q: solve using the appropriate method. y + 3y − 1/ t = t + 2

A: y+3y-1t=t+2y+3y-1t-y+3y=t+2-y+3ySimplify: -1t=t+2-4yMultiply t: -1tt=tt+2t-4ytSimplify: -1=t2+2t-4yt

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: Q2\Using the variation of parameter , find the solution of: y'+9y= sec3x

A: Particular solution by variation of parameter where W is wronskian of y1 and y2.

Q: y" – 6y' + 9y = :

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Q: Q6- By using Direct metheds solve the lineair algebric Equatione- 15 X + 3 y + 27 = 85 X - 2 y + 82=…

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Q: 4. y' + 4y = x?

A: Given information: y' +4y=x2

Q: y'-2y/x=x^2e^x x=1 and y=0 solve using linear equation (diff eq

A: Given :y'-2xy=x2ex

Q: Find the general solution for the equation dy a² + (xy)- 2.ry + y? dr

A: The differential equation is given as x2+(xy)dydx = 2xy+y2xy dydx = 2xy+y2-x2dydx = 2xy+y2-x2xy…

Q: Solve the equation: å oy = Esimpt t ezt-X %3D

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Q: Solve Hhe follaing notúel vale prodlems y's x+ 2e*", gl9) = 4.

A: Consider the initial value problem  y'=x+2ex−9,                  y9=4

Q: Solve y"-xy' - By = 0, x>0 A) y = e+ B) y = c,x* + C) y= + D) y =c,3r*+

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Q: 1. Solve for y. D B 420 C0y-4 8. Find MZBCD. 40

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Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: Differntiate the equation implicity to find p' (x). r'p+xp+1 2x+p 3D1

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Q: Find the solution using variation of parameters to the diffrential equation (D3 + D)y = sec2x

A: Find the solution using variation of parameters to the diffrential equation (D3 + D)y = sec2x

Q: y= 2x³-27 3x4 - 2x Find dy da

A: Given: y=2x5-x33x4-2xTo Find: To find dydx.

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: Solve for the values of Ay and dy if y= f(x) =x² + 2x? – 3x + 5 and x changes from 2 to 2.10.

A: Given: y=fx=x3+2x2-3x+5 And x1=2 &  x2=2.10  a). We know that; ∆y=yx2-yx1 So,…