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Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0

dy/dx = (dy/du) (1/x), d^2(y)/dx^2 = (d^2(y)/du^2) (1/(x^2)) - (dy/du)*(1/(x^2)) (x^2) ( (d^2(y)/du^2) (1/(x^2)) - (dy/du) (1/(x^2)) ) + x (dy/du)*(1/x) + y = 0 d^2(y)/du^2 - dy/du + dy/du + y = 0 d^2(y)/du^...
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Solve (x+2)/3x + (x-2)/2x = 3

In order to solve this equation we need to rearrange it to have all of the variables on one side of the equals sign and the constants on the other. We do this by multiplying each term by the denominator of o...
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Answered by Annabel Y. Maths tutor
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How do I solve simultaneous equations?

A easy way to solve simultaneous equations is to substitiute one equation into another and then equate to find one of the unknowns. Once this has been found its a simple matter of substituting it back into t...
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Answered by Kishen L. Maths tutor
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Why do branch chained isomers have lower boiling point than straight chain equivalents?

As branching increases the boiling point decreases because there are fewer points of contact. This also means van der Waals forces are weaker in branch chained isomers and thus less energy is required to ove...
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Answered by Kishen L. Chemistry tutor
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What are the stages of cell division?

Cell division occurs through a process called mitosis where a mother cell splits in two to form daughter cells identical to that of the mother. The stages of mitosis are prophase, metaphase, anaphase, teloph...
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Answered by Kishen L. Biology tutor
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