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Please Solve R.D.Sharma class 12 Chapter 21  Differential Equations Exercise Revision Exercise Question 21 Maths textbook Solution.

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Hint: Apply integration to find the equation

Given:  \frac{dy}{dx}+4x=e^{x}

Solution:  \frac{dy}{dx}+4x=e^{x}

              \begin{aligned} &\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{\mathrm{x}}-4 \mathrm{x} \\ &\Rightarrow \mathrm{dy}=\left(\mathrm{e}^{\mathrm{x}}-4 \mathrm{x}\right) \mathrm{dx} \end{aligned}

             integrate both sides

             \begin{aligned} &\Rightarrow \int d y=\int\left(e^{x}-4 x\right) d x \\ &\Rightarrow \quad y=e^{x}-4 * \frac{x^{2}}{2}+c \\ &\Rightarrow \quad y=e^{x}-2 * x^{2}+c \\ &\Rightarrow \quad y+2 x^{2}=e^{x}+c \end{aligned}


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