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Find the solution the the differential equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x)

We first find the complementary function by guessing y=e^(kx). Substituting this into the equation d^2y/dx^2 + (3/2)dy/dx + y = 0. we find k^2 + (3/2)k + 1 = 0 which factorises into (k+2)(k+1/2). So our comp...
NE
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Solve the following set of simultaneous equations: 3x + 2y = 15 & 9x + 4y = 1

Label your equations 1 and 2. Look to eliminate one of your variables to create a third equation with only one variable. To do this multiply the first equation by 2 to obtain: 6x + 4y =30 *Label as equation ...
CA
Answered by Chris A. • Maths tutor
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How important are quotes in an essay? How do I go about learning/applying them?

Learning and implementing quotations are and always will be a necessary evil in academic writing. However, whether it be from the primary source or a secondary critic, they are invaluable in supporting and v...
JD
10630 Views

How does electrical activity of the heart cause the heart to pump?

The sinoatrial (SA) node is a group of specialized cells which sit in the wall of the right atrium. The SA node sets the pace of your heart and is therefore called your pacemaker. SA node sets this pace by g...
NE
Answered by Nithya E. • Biology tutor
3314 Views

Find the equation of the tangent at x=1 for the curve y=(4x^2+1)^3

The tangent is the straight line passing through x=1, touching the curve only at that point. For x=1, y=(4+1)^3=125 Using the chain rule we obtain dy/dx = 3 8x (4x^2+1)^2. To then get the gradient of the tan...
JH
Answered by Jacob H. • Maths tutor
4066 Views