Differential equations class 12 ncert solutions
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It is given that the principal increases continuously at the rate of 5% per year. Page No 406: Answer: Therefore, the given differential equation is a homogeneous equation. The highest power raised to is 1. There increasing and decreasing functions, approximation with a maximum and minimum derivatives. In which, get its general solution by replacing P from C.

This is a polynomial equation in and and the highest power raised to is one. Then you will find the equation of a curve that is passing through a specific location with the help of given parameter. Apart from the clearing the doubts, students can also have a deeper understanding of the concepts from this chapter and get to know the best answers to the respective questions. Substituting in equation 2 , we get: This is the required solution of the given differential equation. It is a polynomial equation in and the power raised to is 1. Hence, an indepth study of differential equations has assumed prime importance in all modern scientific investigations.

Answer : Let the rate of change of the volume of the balloon be k where k is a constant. If you want to prepare for more better performance in your examinations then these books can help you. You will learn all of these my some assumption questions and then solutions. The highest power raised to is one. Hence, the given function is the solution of the corresponding differential equation. The given differential equation is not a polynomial equation in its derivatives.

In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present? It has gotten 1804 views and also has 4. Find the equation of a curve passing through the point 0, 2 given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5. However, the given differential equation is not a polynomial equation. The highest power raised to is 2. Hence, its degree is one.

Answer : The differential equation of the given curve is: Integrating both sides, we get: Now, the curve passes through point 1, -1. Hence, the correct answer is C. Hence, the given function is the solution of the corresponding differential equation. It is given that the rate of growth of the bacteria is proportional to the number present. Therefore, its order is two. Hence, its degree is not defined. Q4 : Answer : Differentiating both sides with respect to x, we get: Multiplying equation 1 with equation 2 and then subtracting it from equation 2 , we get: Differentiating both sides with respect to x, we get: Dividing equation 4 by equation 3 , we get: This is the required differential equation of the given curve.

Answer: Let the population at any instant t be y. It is given that it passes through point —2, 1. The differential equation of the family of circles with centre at 0, b and radius 3 is as follows: Differentiating equation 1 with respect to x, we get: Substituting the value of y — b in equation 1 , we get: This is the required differential equation. For each of the exercises given below, verify that the given function implicit or explicit is a solution of the corresponding differential equation. Answer : Integrating both sides, we get: Hence, the correct answer is A.

The highest power raised to is 1. Let a, 0 be the centre of the circle. Therefore, its order is two. Hence, its degree is 2. Thus, its order is two.

Now, the equation of the circle with centre a, 0 and radius a is Differentiating equation 1 with respect to x, we get: Now, on substituting the value of a in equation 1 , we get: This is the required differential equation. Solutions of Differential Equations of the First Order and First Degree A differential equation of first degree and first order can be solved by following method. The differential equation of the family of circles with centre at 0, b and radius 3 is as follows: Differentiating equation 1 with respect to x, we get: Substituting the value of y — b in equation 1 , we get: This is the required differential equation. It is a polynomial equation in. Q2 : Answer : The given differential equation is The solution of the given differential equation is given by the relation, This is the required general solution of the given differential equation.

Page No 397: Answer: Let p, t, and r represent the principal, time, and rate of interest respectively. It is given that the rate of growth of the bacteria is proportional to the number present. Q3 : Answer : The given differential equation is: The solution of the given differential equation is given by the relation, This is the required general solution of the given differential equation. After that you will be learning about binary operation, composite function, inverse function and so on. Thus, its order is four. In this chapter you will learn the different type of relations like: symmetric, transitive, equivalence and reflexive.