Question 8 of 96beginner💡 UnderstandVery Short1 mark

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

y′+y=exy' + y = e^x
Correct Answer

Order = 1, Degree = 1

Exercise: EXERCISE 9.1 | Q: 8 | (Page 4)
For More Understanding

Explanation

Following the method shown in Example 1(i) of the textbook, we identify the highest order derivative present in the differential equation. The equation y' + y = exe^{x} contains only y' (which is dy/dx), a first-order derivative. Hence, the order is one. The equation is a polynomial equation in y' (the derivative appears linearly without being inside any transcendental function), and the highest power raised to y' is one. Therefore, the degree is one.

Solution Steps

  1. Step 1: Identify the highest order derivative present in the equation y' + y = exe^{x}. The only derivative is y' (first-order).

  2. Step 2: Therefore, Order = 1.

  3. Step 3: Check if the equation is a polynomial in derivatives. Yes, y' appears linearly (to the power 1).

  4. Step 4: Therefore, Degree = 1.

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