Engng Maths 214 Linear Substitutions

Linear substitutions

For DEs of form dy/dx = f(ax + by + c)

use u = ax + bx + c (denominator or numerator)

du = a dx + b dy

Solving using linear substitution

• Multiply du equation by 1/dx → du/dx = a + b dy/dx

• Replace dy/dx with your equation & substitute in u

• Write in terms of du/dx (combine terms with fraction so that flipping fraction in next step possible)

• Solve SDE (+ C)

• Sub back and write in terms of y

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