Class 12 CBSE Applied Maths Differential Equations Exercise 8.3

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 8.1 Exercise 8.2 Exercise 8.4 Exercise 8.5 Case Study

Q1. (i) Write the order of the differential of the family of circles x2 + y2=a2, where a (>0) is arbitrary constant.

(ii) Write the order of the differential equation of the family of parabolas y² = 4ax, where a is arbitrary constant.

(iii) Write the order of the differential equation of the family of parabolas y² = 4a (x - b), where a, b are arbitrary constants.

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Q2. (i) Form the differential equation of the family of straight lines y = mx, where m is arbitrary constant.

(ii) Find the differential equation of the family of straight lines y = mx + c, where m, c are arbitrary constants.

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Q3. Form the differential equation of the family of concentric circles x2 + y² = r², where r(>0) is arbitrary constant.

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Q4. Form the differential equation not containing the arbitrary constant(s) and satisfied by the following equations:

(i) y=ax3, a is arbitrary constant

(ii) x2- y2=a2, a is arbitrary constant
(iii) y2=4ax, a is arbitrary constant

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Find the differential equations by eliminating the arbitrary constants and satisfied by the following (5 to 8) equations:



Q5. (i) x²+(y-b)2=1, b is arbitrary constant

(ii) x²+ y²= ax³, a is arbitrary constant.

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Q6. x/a+y/b=1, a, b are arbitrary constants.

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Q7. y2=4a (x-b), a, b are arbitrary constants.

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Q8. y=Ae2x+Be-2x, A, B are arbitrary constants.

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Q9. Find the differential equation of each of the following family of curves: (i) concentric circles with centre at (1, 2).

(ii) all circles which touch the x-axis at origin.

(iii) circles in the first quadrant and touching the coordinate axes.

(iv) all parabolas having their vertices at origin and foci on y-axis.

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Q10. Form the differential equation of the family of circles having centres on y-axis and radius 3 units

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