Engng Maths 214 Homogeneous DEs

Homogeneous DEs

• homogeneous if all terms are of same degree

• ln() & e⁽⁾ don’t count

• Multiplying, dividing, roots, exponents affect degree

Substitution for HDEs

y = ux

dy = udx + xdu

Solving HDEs

• Check if homogeneous

• Multiply dy equation by 1/dx => dy/dx = u + x du/dx

• Make substitutions

• Divide out common term

• Solve SDE (has +C)

• Substitute original variables back

Simplifying step using e^f(x)

When using e on both sides of equation to get rid of ln(…):

e can NOT be applied to each term individually. Apply e to ENTIRE LHS and RHS then simplify using e properties!