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  • Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 46 textbook solution.

Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 46 textbook solution.

Answers (1)

Answer : (c) \frac{d^{2} y}{d x^{2}}-x^{2} \frac{d y}{d x}+x y=0

Hint : Check each options one by one .

Given : y=x

Explanation : y=x

\begin{aligned} &\Rightarrow \frac{d y}{d x}=1 \\ &\Rightarrow \frac{d^{2} y}{d x^{2}}=0 \end{aligned}

Now, option  (a)\frac{d^{2} y}{d x^{2}}-x^{2} \frac{d y}{d x}+x y=x

\begin{aligned} &\text { LHS }=0-x^{2} \times 1+x \times x \\ &=-x^{2}+x^{2}=0 \neq x \end{aligned}

Option \text { (b) } \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+x y=x

\begin{aligned} &\text { LHS }=0+x \times 1+x \times x=x \\ &=x+x^{2} \neq x \end{aligned}

Option \text { (c) } \frac{d^{2} y}{d x^{2}}-x^{2} \frac{d y}{d x}+x y=0

\begin{aligned} &\text { LHS } \\ &\qquad \begin{array}{l} =0-x^{2} \times 1+x \times x \\ =-x^{2}+x^{2} \\ =0=\mathrm{RHS} \end{array} \end{aligned}

Hence, the correct option is (c)

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