Using the method of undetermined coefficients, solve the differential equation:

Using Charpit's method, find the complete integral of the p.d.e.:

Solve: . 

Find the integral surface of the p.d.e.:

through the circle . 

Suppose that a thermometer having a reading of  inside a house is placed outside where the air temperature is . Two minutes later it is found that the thermometer reading is . Find the temperature reading T(t) of the thermometer at any time t. 

Apply the method of variation of parameter to solve the differential equation:

 The Pfaffian equation  is integrable.

The solution of the differential equation

 with 

exists, but is not unique.

  in  is a linear homogeneous equation

 The solution of the differential equation  with  exists, but is not unique.

 State whether the following statements are true or false. Justify your answer with the help of a short proof or a counter example: 
a) y² is an integrating factor of the differential equation:

.

give two errors that this child may make while learning this process. How would you use these errors to her learning?

formulate three questions to draw out her thinking.

 how would you access her readiness for this topic?

Suppose you are teaching a child addition of decimal fractions, according to the constructivist model. In this context,

 What is ‘egocentrism’? What did Martin Hughes think about Piaget’s views on egocentrism? What was the experiment which his understanding was based on?

. Why do we need to develop the ability of estimating the outcome of arithmetic operations on fractions? Further, give a series of three activities to help a Class 4 child develop the ability to estimate the bigger of two fractions. Explain how the activities form a series.

Gathering data is one tool for making sense of the world around.

) Developing spatial understanding is more than about learning some definitions and rules of geometry.

A teacher should be a scaffold for her learners.