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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 12 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 12 Maths Textbook Solution.

Answers (1)

Answer:  Hence verified

Hint: Find first and second derivative of given equation and put in differential equation to be verified.

Given: y=cx+2c^{2}\; \; \; \; ,2\left ( \frac{dy}{dx} \right )^{2}+x\frac{dy}{dx}-y=0

Solution:  y=C\: x+2\: c^{2}

\frac{dy}{dx}=c…differentiating w.r.t to x

\frac{d^{2}y}{dx^{2}}=0..differentiating agin w.r.t to x

Now, differential equation is

\begin{aligned} &2\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+x \frac{\mathrm{dy}}{\mathrm{dx}}-\mathrm{y}=0 \\ &\mathrm{~L} . \mathrm{H} \cdot \mathrm{S}=2(\mathrm{c})^{2}+\mathrm{x}(\mathrm{c})-\mathrm{c} x-2 \mathrm{c}^{2} \\ &=2 \mathrm{c}^{2}+\mathrm{c} \mathrm{x}-\mathrm{c} \mathrm{x}-2 \mathrm{c}^{2}=0=\mathrm{R} . \mathrm{H} . \mathrm{S} \end{aligned}

Hence verified

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