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  • Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.3 question 14

Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.3 question 14

Answers (1)

Answer:

y=-x-1  is a solution of differential equation

Hint:

Differentiate the solution and modify the given differential equation

Given:

y=-x-1

Solution:

Differentiating on both sides with respect to x

\begin{aligned} &\frac{d y}{d x}=-\frac{d(x)}{d x}-\frac{d(1)}{d x} \\\\ &\frac{d y}{d x}=-1 \end{aligned}            ...............(i)

Now the given equation has to be modified

\begin{aligned} &(y-x) d y-\left(y^{2}-x^{2}\right) d x=0 \\\\ &(y-x) d y=\left(y^{2}-x^{2}\right) d x \\\\ &\frac{d y}{d x}=\frac{y-x}{y^{2}-x^{2}} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{y-x}{(y-x)(y+x)} \\\\ &\frac{d y}{d x}=\frac{1}{y+x} \end{aligned}            ..............(ii)

Comparing equation (i) and (ii)

\begin{aligned} &\frac{1}{y+x}=-1 \\\\ &1=-(y+x) \\\\ &y=-x-1 \end{aligned}

Thus,it is proved that y=-x-1 is a solution of differential equation.

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