📐 Mathematics · Differential Equations · JEE

The integrating factor for dy/dx + Py = Q (P, Q functions of x) is:

Answer: e^{integral of P dx}.

A e^{integral of Q dx}
B e^{integral of P dx}
C P × Q
D 1/P

Correct answer: B. e^{integral of P dx}

Explanation: Linear first-order DE: integrating factor = e^{integral P dx}. Multiply both sides to make LHS exact.

The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.

Concept context

Equations involving derivatives and their solutions

Read the full Differential Equations notes →

The integrating factor for dy/dx + Py = Q (P, Q functions of x) is:

Concept context

More Differential Equations questions