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Need solution for RD Sharma Maths Class 12 Chapter 21 Differential Equation Excercise 21.10 Question 6

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Answer:  y=(2 x-1)+C e^{-2 x}

Hint: To solve this equation we will use differentiate different.

Give:  \frac{d y}{d x}+2 y=4 x

Solution:  \frac{d y}{d x}+P y=Q

\begin{aligned} &P=2, Q=4 x \\ & \end{aligned}

I\! f=e^{\int P d x} \\

=e^{\int 2 d x} \\

=e^{-2 x} \\

\begin{aligned} &y e^{2 x}=\int 4 x e^{2 x} d x+C \\ \end{aligned}

y e^{2 x}=4 \int x e^{2 x} d x+C \\

y e^{2 x}=4\left[\frac{x e^{2 x}}{2}\right]-\left[\frac{e^{2 x}}{2} d x\right]+C \\

y e^{2 x}=2 x e^{2}-2 \frac{e^{2 x}}{2}+C \\

y=(2 x-1)+C e^{-2 x}

y \times I f=\int Q \times \operatorname{If} d x+C

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