MHT CET202013 Oct 2020Morning ShiftMathematicsDifferential EquationsActual
The equation of the curve which passes through point (1,0) and has tangent with slope 1+ y x + ( y x )² is
Options
- A⁻¹ ( x y )= |x|
- B⁻¹ ( x y )= |y|
- C⁻¹ ( y x )= |y|
- D⁻¹ ( y x )= |x|
Correct answer
D. ⁻¹ ( y x )= |x|
Step-by-step solution
We have siope of tangent = d y d x =1+ y x + ( y x )² d y d x =1+ y x + y² x² d y d x = x²+x y+y² x² ...(1) Put y=u x d y d x =u+x d u d x u+x d u d x = x²+u x²+u² x² x² u+x d u d x =1+u+u² x d u d x =1+u² d u 1+u² = d x x ⁻¹ u= |x|+c ⁻¹ ( y x )= |x|+c At (1,0) , we write ⁻¹(0)= |1|+c c=0 ⁻¹ ( y x )= |x|