Problem 12 Easy Difficulty

Which of the following differential equations has $y=x$ as one of its particular solution?
(A) $\frac{d^{2} y}{d x^{2}}-x^{2} \frac{d y}{d x}+x y=x$
(B) $\frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+x y=x$
(C) $\frac{d^{2} y}{d x^{2}} x^{2} \frac{d y}{d x} x y \quad 0$
(D) $\frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+x y=0$

Answer

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Calculus 2 / BC

NCERT Class 12 Part 2 - Math

Chapter 9

Differential Equations

Section 3

General and Particular Solutions of a Differential

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Video Transcript

we know determine the correct differential equation. We just a particular solution, Y equal to X. So how we do this is we take this Y equal to x differentiated couple of frames. And using those equations as well as the equal rights we substitute in each of the options and verify which one sells or which one satisfies. So let's take the first equation. Why equal to X. We differentiate this once will be getting the way by the X. Only differentiate why with respect to X. And when you differentiate X with respect to X we get one. We differentiate this one more time. So we'll be getting de tu Y by B X two. This is equal to differentiating one will get zero. So we know how this three questions. You're going to substitute in each of the options. So let me substitute in the option A We have a need to Y by dx to which I can support this as zero minus of X squared. Do everybody X. I can substitute one for this. Plus extends Hawaii I can substitute X in place of white. So this we have X on the right hand side. So when you simplified this side I'll be getting negative X squared plus X squared is equal to X Which means the side I get zero is equal to X. zero Equal Rex. No this is not true. So we mark this as not true. Which means option is not the correct differential equation. So let's move on to the option B. So here we substitute 42 y body extra which is zero plus extends of the web addicts. That is I can substitute one for this one Plus extreme software that is X. Repressed by by X. So this is equal to X. This verify if both sides are matching that is X plus X squared is equal to X. So they said we have express exclude and they said we have X. So these two sides are not equal so we can work. This is not true which means the option B is also not the correct one. So now let's verify for option C. It's an option C. We have a detail why by the X squared that is zero -X squared of diva videos that is one plus X terms of why can replace their ex Let's see if we get zero. So this is negative, X squared plus X squared is equal to zero which means this is 90 X squared plus x squared is zero. So we can mark this as zero. This site which means zero equal to zero which is true in fact, so therefore option C is the correct answer. And the two Y BD x squared minus X squared. Everybody explosives were equal to zero is the correct differential equation which has the particular solution why equal to X.

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