$\frac{y d y}{d x} + x y = x^{2}$ is a linear differential equation of first order.

True

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False

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Solution

The correct option is B False
What is a linear differential equation? A linear ODE satisfies the following conditions:
1- The dependent variable y and its derivatives occur to the first degree only.i.e, their power will be always one.
2- No products of y and/or any of its derivatives appear in the equation.
3- No transcendental functions of y or its derivatives occur.
As per the point 2 In A linear differential equation there should not be any products of dependent variable y and its derivative. In the given equation you can see that in the first term itself y and its derivative are multiplied. So it is not a linear differential equation.
It should be of the form $\frac{d y}{d x} + P (x) y = Q (x)$

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