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  • Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 39

Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 39

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Answer: y^{2}=4|\sec 2 x|

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

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

Solution:\frac{d y}{d x}=y \tan 2 x, y(0)=2

        \frac{d y}{y}=\tan 2 x d x

        Integrating both sides

        \begin{aligned} &\int\left(\frac{d y}{y}\right)=\int \tan 2 x d x \\\\ &\log y=\frac{1}{2} \log |\sec 2 x|+c \\\\ &y(0)=2 \text { where, } y=2 \; \& \; x=0 \end{aligned}

        \begin{aligned} &\log (2)=\frac{1}{2} \log |\sec 2(0)|+c \\\\ &c=\log 2 \\\\ &\log y=\frac{1}{2} \log |\sec 2 x|+\log 2 \end{aligned}

        \begin{aligned} &\log y=\log \sqrt{\sec 2 x}+\log 2 \\\\ &y=2 \sqrt{\sec 2 x} \\\\ &y^{2}=4|\sec 2 x| \end{aligned}

        

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