CBSE Class 12 Mathematics Differentials Equation Worksheet Set A

CBSE Class 12 Mathematics Differentials Equation Worksheet Set A

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1) Form the differential equation of the family of circles touching y axis at origin. What are the values conveyed by the family of circles formed?

Ans: y² – x² – 2xyy1 = 0 . Bond, integrity , inter relationship, understanding.

2. The temperature T of a cooling object drops at a rate which is proportional to the difference T-S, where S is the constant temperature of the surrounding medium. Thus dT/dt = -k (T – S) ,where k > o is a constant and t is the time. Solve the differential equation if it is given that T(0) =150. What are the demerits of global warming?

Ans: T-S/150-S = e-kt . Abnormal weather conditions, frequent occurrence of tremors, earthquakes and tsunami.

3. Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y-axis. Mosquito bite is the origin for `Dengue’ . Suggest two methods to curb the breeding of mosquitoes.

Ans: xy¹-2y=0. To avoid stagnation of water.

To keep the environment hygienic.

4. Show that the given differential equation is homogeneous and solve it.

X² dy+ y (x+y) dx = 0.

Which is advantageous to life homogeneity or hetrogenity ? Justify your answer.

Ans : y + 2x = 3x²y.

Homogenity : equal rights, uniformity, oneness.

Hetrogenity : independently thinking and acting individuals who work for the society.

Unity in diversity.

5. Solve the differential equation

X ( x² – 1 ) dy/dx =1 ; y =0 when x = 2

If `y’ is distance and x is the time. dy/dx is velocity.

Ravi rides a vehicle beyond the limit in a highway. What suggestions would you give him to help him understand the risks of overspeeding?

Ans : y = ½ log [x²-1/x²] – ½ log ¾.

Ravi would be told about the road safety and traffic regulations.Also should be made understand that ` speed thrills but kills ‘.