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Differential Equations

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An equation of the form dy/dx=f(ax+by) can be transformed into an equation with seperable variables by making substitution z=ax+by or z=ax+by+c. use this technique to solve.

y' = sqrt (4x + 2y - 1)

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The expert examines differential equations using separable variables by making substitution. A complete, neat and step-by-step solution is provided.

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Let 4x + 2y - 1 = z

Then 4 + 2(dy/dx) = dz/dx

dy/dx = [(dz/dx) - 4] / 2 = (1/2)(dz/dx) - ...

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