Question

Which sequence correctly states the essential actions for obtaining the final answer of a homogeneous differential equation?

Options

• Integrate first; choose \[\lambda=0\]; differentiate the final answer; remove \[v\].

• Choose \[x+y\]; differentiate without the product rule; avoid separation; keep \[v\].

• Check homogeneity first; differentiate substitution carefully; convert to separable form; back-substitute to original variables.

• Back-substitute first; convert to degree \[0\]; integrate only \[x\]; check \[\lambda\].

Answer 1

Homogeneity must be checked before applying the substitution. The substitution is differentiated carefully, the equation is converted to separable form and integrated, then \[v\] is back-substituted to original variables.