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Please Solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 3 Maths Textbook Solution.

Answers (1)

Answer:  y e^{2 x}=2 e^{3 x}+C

Hint: To solve this equation we use  \frac{d y}{d x}+P y=Q  formula

Give:  \frac{d y}{d x}+2 y=6 e^{x}

Solution:   \frac{d y}{d x}+2 y=6 e^{x} \cdot \cdot \cdot \left ( i \right )

\frac{d y}{d x}+P y=Q

\begin{aligned} &P=2, Q=6 e^{x} \\ \end{aligned}

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

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

=e^{2 x} \\

=y \times I f=\int(I f \times Q) d x \\

=y \times e^{2 x}=\int e^{2 x} \times 6 e^{x} d x \\

=y e^{2 x}=6 \int e^{3 x} d x \\

=y e^{2 x}=\frac{6}{3} e^{x}+C \\

=y e^{2 x}=2 e^{x}+C



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