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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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