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Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 48 textbook solution.

Answers (1)

Answer :  (c)x=vy

Hint : Take x=vy

Given : \frac{dx}{dy}=h(\frac{x}{y})                               ....(i)

Explanation : Let x=vy

\Rightarrow \frac{d x}{d y}=v+y \frac{d v}{d y}

Put in (i)

\begin{aligned} &\Rightarrow v+y \frac{d v}{d y}=h(v) \\ &\Rightarrow y \frac{d v}{d y}=h(v)-v \\ &\Rightarrow \frac{d y}{y}=\frac{d v}{h(v)-v} \end{aligned}

Is homogeneous

Hence, x=vy

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