Question
What is the solution of the differential equation ( dy dx )=p when y(0)=q ?
NDA
Mathematics
Differential Equations
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. ( y-q x )=p
- B. ( y-p x )=q
- C. ^ -1 ( y-q x )=p
- D. ^ -1 ( y-p x )=q
Answer
A. ( y-q x )=p
Step-by-step solution
The given differential equation is ( dy dx )=p dy dx = ^ -1 (p) Integrating both sides with respect to x, we get: y = x ^ -1 (p) + C Given y(0) = q, substituting x = 0 and y = q: q = 0 + C C = q Substituting the value of C in the equation: y = x ^ -1 (p) + q y - q = x ^ -1 (p) y - q x = ^ -1 (p) ( y - q x ) = p Answer: ( y-q x )=p
Related: Mathematics — Differential Equations · All PYQ Banks