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Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0

As we know, a general solution for a given differential equation is the complimentary solution + the particular solution/integral, this case is no different. To solve for the complimentary solution, form the...
AG
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Describe the reflex arc in response to the hand touching a burning hot stove. Include the names and a description of location and function of all neurons involved. Bullet points are sufficient.

All bold text gives marking points Stimulus (burning hot stove) Receptor (thermoreceptor in skin) detects stimulus Sensory neurone - relays sensory information in the form of electrical impulses from recepto...
JV
Answered by Jonathan V. • Biology tutor
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LOWER TIER a) Multiply the following out: (x+3)(x-4). b) Factorise the following equation into two bracket form: x^2+7x+12

a) Use FOIL to multiply out these bracketsF: x 2 O: -4xI: +3xL: -12 x 2 -4x+3x-12 = x 2 -x-12b) Find two common numbers that ADD UP to give +7, and MULTIPLY TOGETHER to give 12 MULTIPLY TO 12 1 and 122 and 6...
JV
Answered by Jonathan V. • Maths tutor
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HIGHER TIER a) Factorise the following equation into two bracket form: 2x^2-5x-12. b)2x^2-5x-12=0. Solve this equation to find the values of x, using your answer to part a). BONUS c) Sketch the function y=2x^2-5x-12, showing any x intercepts

a) Find two common numbers that ADD UP to give -5, and MULTIPLY TOGETHER to give (2*-12=) -24 MULTIPLY TO -24 -1 and 24 1 and -24 -2 and 12 2 and -12 3 and -8 -3 and 8 4 and -6 - 4 and 6 ADD TO -5 5 and -10 ...
JV
Answered by Jonathan V. • Maths tutor
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Solve the equation ((2x+3)/(x-4)) - ((2x-8)/(2x+1)) = 1. Give your answer to 2 decimal places.

Multiply both sides of the equation by the denominators to get:(2x+3)(2x+1) - (2x-8)(x-4) = (x-4)(2x+1)Expand all the brackets to get:(4x^2 + 6x + 2x + 3) - (2x^2-8x-8x+32) = 2x^2-8x+x-4Simplify both sides t...
NS
Answered by Natalie S. • Maths tutor
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