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Please solve RD Sharma class 12 chapter Differential Equations exercise 21.7 question 45 sub question (v) maths textbook solution

Answers (1)


Answer: x^{2}=\log y

Hint: Separate the terms of x and y and then integrate them.

Given: \frac{d y}{d x}=2 x y, y(0)=1


        \begin{aligned} &\frac{d y}{d x}=2 x y \\\\ &\Rightarrow \frac{d y}{y}=2 x d x \end{aligned}

        Integrating both sides

        \begin{aligned} &\int \frac{1}{y} d y=\int 2 x d x \\\\ &\Rightarrow \log y=\frac{2 x^{2}}{2}+c \Rightarrow \log y=x^{2}+c \end{aligned}        .............(1)

        Given that at  x=0, y=1

        \therefore \log 1=0+c \Rightarrow 0=0+c \Rightarrow c=0 \quad[\therefore \log 1=0]

        Put in (1) we get

        \log y=x^{2}+0 \Rightarrow x^{2}=\log y

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