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

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

Answers (1)

Answer:y+2x^{2}=e^{x}+c

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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