Q68.The general solution of the differential equation √1 + x2 + y2 + x2y2 + xy dxdy = 0 (where C is a constant of integration) + C (1) √1 + y2 + √1 + x2 = 12 loge( √1+x2+1√1+x2−1 ) + C (2) √1 + y2 −√1 + x2 = 12 loge( √1+x2+1√1+x2−1 ) + C (3) √1 + y2 + √1 + x2 = 12 loge( √1+x2−1√1+x2+1 ) (4) 1 √1+x2+1 + C √1 + y2 −√1 + x2 = 2 loge( √1+x2−1 )
What This Question Tests
The question tests the ability to solve a first-order differential equation by separating variables and then integrating standard forms.
Concepts Tested
Formulas Used
∫ (1/√(1+y^2)) dy = log|y + √(1+y^2)|
∫ (x/√(1+x^2)) dx = √(1+x^2)
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📋 Question Details
- Chapter
- Differential Equations
- Topic
- Variable Separable Differential Equations
- Year
- 2020
- Shift
- 06 Sep Shift 1
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 9: Differential Equations
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