Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2015MathematicsInverse Trigonometric Functions

The solution of differential equation [ x d y d x +2 y=x² is ]

Options

  1. A( y= x²+C 4 x² )
  2. B( y= x² 4 +C )
  3. C( y= x⁴+C x² )
  4. D( y= x⁴+C 4 x² )

Correct answer

D. ( y= x⁴+C 4 x² )

Step-by-step solution

Given differential equations, [ array l x d y d x +2 y=x² d y d x + 2 y x =x (1) array ] General differential equation of this type is given by [ d y d x +P(x) y=Q(x) ] So, ( P= 2 x ) then I.F. factor is given by [ e^ P d x =e^ 2 x d x =e^ 2 x =e^ x² =x² ] Then, ( x² d y d x +2 x y=x³ ) [ d d x (x² y )=x³ ] Integrating both the sides, we get [ array l x² y= x⁴ 4 +C₁ x² y= x⁴+C 4 y= x⁴+C 4 x² array ]

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All KCET PYQs