NDA2026MathematicsDifferential EquationsActual
What is the solution of the differential equation ( dy dx )=p when y(0)=q ?
Options
- A( y-q x )=p
- B( y-p x )=q
- C⁻¹ ( y-q x )=p
- D⁻¹ ( y-p x )=q
Correct 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