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  • Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 32 maths textbook solution.

Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 32 maths textbook solution.

Answers (1)

Answer : y=x^{2}+Cx

Hint : The differential equation is linear in y.

Given : x\frac{dy}{dx}-y=x^{2}

Explanation : Divide both sides by x

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

So, the given differential equation is linear in y

\begin{gathered} I F=e^{\int-\frac{1}{x} d x} \\ \quad=e^{-\log x} \\ \quad=\frac{1}{x} \end{gathered}

The general solution is

\begin{aligned} &\Rightarrow y \frac{1}{x}=\int x \frac{1}{x} d x+C \\ &\Rightarrow \frac{y}{x}=\int d x+C \\ &\Rightarrow \frac{y}{x}=x+C \end{aligned}

\begin{aligned} &\Rightarrow y=x(x+C) \\ &\Rightarrow y=x^{2}+C x \end{aligned}

Note: Option b is not matching with final answer.

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