JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023Let the solution curve x = x(y), 0 < y < \frac{\pi}{2}, of the differential equation (loge(cosy))2cosydx−(1+3xloge(cosy))sinydy=0 satisfy x(3π)=2loge21. If x(6π)=logem−logen1, where m and n are co-prime, then mn is equal to
Choose the correct answer:
- A.
12
(Correct Answer) - B.
11
- C.
10
- D.
9
12
Explanation
Given Equation:
Step 1: Rearranging to standard linear form
Step 2: Finding the Integrating Factor (I.F.)
This is a linear differential equation of the form dydx+Px=Q.
Let u=lncosy⟹du=−tanydy.
Step 3: General Solution
Solving the integral (using substitution u=lncosy):
Step 4: Boundary Condition
At y=3π,
Step 5: Finding the constant C
Step 6: General Equation with C=0
Step 7: Calculating x at y=6π
Step 8: Simplifying the expression for x
Final Result:
Explanation
Given Equation:
Step 1: Rearranging to standard linear form
Step 2: Finding the Integrating Factor (I.F.)
This is a linear differential equation of the form dydx+Px=Q.
Let u=lncosy⟹du=−tanydy.
Step 3: General Solution
Solving the integral (using substitution u=lncosy):
Step 4: Boundary Condition
At y=3π,
Step 5: Finding the constant C
Step 6: General Equation with C=0
Step 7: Calculating x at y=6π
Step 8: Simplifying the expression for x
Final Result:

