In each of the Exercises 1 to 5, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. 1. 1 x y a b 2. y 2 = a (b 2 x 2 ) 3. y = a e 3x + b e 2x 4. y = e 2x (a + bx) 5. y = e x (a cos x + b sin x) 6. Form the differential equation of the family of circles touching the y-axis at origin. 7. Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis. 8. Form the differential equation of the family of ellipses having foci on y-axis and centre at origin. 9. Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin. 10. Form the differential equation of the family of circles having centre on y-axis and radius 3 units. 11. Which of the fol
Question 1:1 x y a b
Question 2:y 2 = a (b 2 – x 2 )
Question 3:y = a e 3x + b e – 2x
Question 4:y = e 2x (a + bx)
Question 5:y = e x (a cos x + b sin x)
Question 6:Form the differential equation of the family of circles touching the y-axis at origin.
Question 7:Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.
Question 8:Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.
Question 9:Form the differential equation of the family of hyperbolas having foci on x-axis and centre at origin.
Question 10:Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Question 11:Which of the following differential equations has y = c1 e x + c2 e –x as the general solution? (A) 2 2 0 d y y dx (B) 2 2 0 d y y dx (C) 2 2 1 0 d y dx (D) 2 2 1 0 d y dx
Question 12:Which of the following differential equations has y = x as one of its particular solution? (A) 2 2 2 d y dy x xy x dx dx (B) 2 2 d y dy x xy x dx dx (C) 2 2 2 0 d y dy x xy dx dx (D) 2 2 0 d y dy x xy dx dx