alleryTo solve a **homogeneous** differential equation of degree 1 (e.g. $dy/dx = f(y/x)$), the standard substitution is:
A$y = x + v$
B$y = vx$
C$y = v + 1/x$
D$y = e^x v$
Answer & Solution
Correct answer: B. $y = vx$
Substitute $y = vx$, so $dy/dx = v + x\,dv/dx$.
This converts the equation to a variables-separable form in $v$ and $x$.
Keep practising Differential Equations
Browse all Differential Equations questions for AP Intermediate 2nd Year, or explore more Mathematics topics.
Related questions
For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:Complete the definition of order and degreeComplete the definition of a differential equationOrder, degree, or neither?True or false: methods of solutionRecognising the typeGeneral solution or particular solution?True or false: what a solution is