1.1. **DIFFERENTIAL** **EQUATIONS** AND SYSTEMS OF **EQUATIONS** 5 (s0 +λt0)∧···∧ (sµ +λtµ) = 0. Expand this with respect to powers of λ. Since we have inﬁnitely many choices for λ the coeﬃcient of every power of λ must be zero. In particular the coeﬃcient of λ. Hence Xµ i=0 s0 ∧···∧ ti ∧···∧ sµ = 0. (1.1) Now put t = x ....

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(iii) The highest order derivative present in the **differential** **equation** is y′′′, so its order is three. The given **differential** **equation** is not a polynomial **equation** in its derivatives and so its degree is not defined. EXERCISE 9.1 Determine order and degree (if defined) of **differential** **equations** given in Exercises 1 to 10. 1. 4 4 sin( ) 0.

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