Class 12 CBSE Applied Maths Differential Equations Exercise 8.2

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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Determine the order and the degree (when defined) of each of the following (1 to 9) Differential equations:

Q1. What is the number of arbitrary constants in the general solution of a differential equation of order 4?

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Q2. What is the number of arbitrary constants in a particular solution of a differential equation of order 3?

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Q3. Verify that y = e^-3x is a solution of the differential equation

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Q4. In each of the following, show that the given function is a solution of the corresponding differential equation:

(i) y = x² + 2x + C : y' - 2x - 2 = 0
(ii) y = Ae^-x : y' + y = 0
(iii) y= √1 + x² : (1 + x²) y' = xy
(iv) y = ae^bx:y"-b²y = 0.

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Q5. Show that the function y = ax + 2a² is a solution of the differential equation

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Q6. Verify that xy = log y + c is a solution of the differential equation (xy − 1) dy/dx + y² = 0.

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Q7. Show that y = e^-x+ ax + b is a solution of the differential equation e^x d²y/dx² =1

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Q8. Show that the differential equation of which y = 2(x²-1) + ce^-x² is a solution is

dy/dx +2xy =4x³

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Q9. Show that y² = 4a (x + a) is a solution of the differential equation y (1 - y²)=2xy₁.

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Q10. Verify that y = ce^-x³ is the solution of the differential equation dy/dx+ 3x²y = 0. Also, determine the solution curve of the given differential equation that passes through the point(0,5)

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Class 12 CBSE Applied Maths Differential Equations Exercise 8.2

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Determine the order and the degree (when defined) of each of the following (1 to 9) Differential equations:

Q1. What is the number of arbitrary constants in the general solution of a differential equation of order 4?

Q2. What is the number of arbitrary constants in a particular solution of a differential equation of order 3?

Q3. Verify that y = e-3x is a solution of the differential equation

Q4. In each of the following, show that the given function is a solution of the corresponding differential equation: (i) y = x² + 2x + C : y' - 2x - 2 = 0 (ii) y = Ae-x : y' + y = 0 (iii) y= √1 + x² : (1 + x²) y' = xy (iv) y = aebx:y"-b²y = 0.

Q5. Show that the function y = ax + 2a² is a solution of the differential equation

Q6. Verify that xy = log y + c is a solution of the differential equation (xy − 1) dy/dx + y² = 0.

Q7. Show that y = e-x+ ax + b is a solution of the differential equation ex d2y/dx2 =1

Q8. Show that the differential equation of which y = 2(x²-1) + ce-x² is a solution is dy/dx +2xy =4x3

Q9. Show that y² = 4a (x + a) is a solution of the differential equation y (1 - y²)=2xy₁.

Q10. Verify that y = ce-x³ is the solution of the differential equation dy/dx+ 3x²y = 0. Also, determine the solution curve of the given differential equation that passes through the point(0,5)

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Q3. Verify that y = e^-3x is a solution of the differential equation

Q4. In each of the following, show that the given function is a solution of the corresponding differential equation:

(i) y = x² + 2x + C : y' - 2x - 2 = 0
(ii) y = Ae^-x : y' + y = 0
(iii) y= √1 + x² : (1 + x²) y' = xy
(iv) y = ae^bx:y"-b²y = 0.

Q7. Show that y = e^-x+ ax + b is a solution of the differential equation e^x d²y/dx² =1

Q8. Show that the differential equation of which y = 2(x²-1) + ce^-x² is a solution is

dy/dx +2xy =4x³

Q10. Verify that y = ce^-x³ is the solution of the differential equation dy/dx+ 3x²y = 0. Also, determine the solution curve of the given differential equation that passes through the point(0,5)