CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Anil Kumar Tondak

CBSE CLASS XII

Differential Equations

Solve the following Differential Equations:

Q. 1. Determine order and degree (if defined) of differential equation   y/// + 2 y// + y/ = 0

Q. 2. sec²x. tany dx + sec²y. tanx dy = 0.

Q. 3. xdy – ydx =

Q. 4. 2xy + y² – 2x² dy/dx = 0,    y = 2 when x = 1.

Q. 5. x logx. dy/dx + y = (2/x) logx

Q. 6. y dx + (x – y²) dy = 0

Q. 7. (tan^-1y -  x)dy = (1 + y²) dx

Q. 8. (1 + x²)dy/dx + 2xy = ;

Q. 9. x²dy + (xy + y²)dx = 0,      y = 1 when x = 1

Q. 10. dx/dy + ycotx = 2x + x²cotx,    y = 0 when x =

Q. 11. (x + y)dy = dx

Q. 12. x (xdy – ydx) = ydx,        y(1) = 1.

Q. 13. dy/dx = cos(x + y) + sin(x + y)

Q. 14. x dy/dx = y – x tan(y/x).

Q. 15. (x² + 1) dy/dx + 2xy =

Q. 16. (x² + y²)dx + xy.dy = 0,    y(1) = 1

Q. 17. (x + y + 1)² dy = dx,        y(-1) = 0

Q. 18. (xy2 + 2x)dx + (x2y + 2y)dy = 0

Q. 19. dy/dx +  = cosx +

Q. 20. Solve the differential equation   

Q. 21. Solve the differential equation  x² dy + y ( x + y ) d x = 0, given that y = 1 when x = 1

Q. 22. Solve:

 Q. 23.

Q. 24.

Q. 25. Find the differential equation of all circles in the first quadrant which touch the co-ordinate axis.

Q. 26. Form the differential equation corresponding to y² = m(a² – x²) by eliminating parameters m and a.

Q. 27. Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

Q. 28. Form the differential equation of the family of circles having centre on y-axis
and radius 3 units.

Paper By Mr. Anil Kumar Tondak
Email Id : [email protected]