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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 15 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 15 Maths Textbook Solution.

Answers (1)

Answer: \frac{d^{3} y}{d x^{8}}-7\left(\frac{d y}{d x}\right)+6 y=0

Hint: The number constants is equals to the number time we differentiate.

Given:  y=ae^{2x}+be^{-3x}+ce^{x}

Solution: y=ae^{2x}+be^{-3x}+ce^{x}

\begin{aligned} &\frac{d y}{d x}=2 a e^{2 x}-3 b e^{-3 x}+c e^{x} \\ &\frac{d^{2} y}{d x^{2}}=4 a e^{2 x}+9 b e^{-3 x}+c e^{x} \\ &\frac{d^{3} y}{d x^{3}}=8 a e^{2 x}-27 b e^{-3 x}+c e^{x} \\ &\frac{d^{3} y}{d x^{3}}=7\left(2 a e^{2 x}-3 b e^{-3 x}+c e^{x}\right)-6\left(a e^{2 x}+b e^{-3 x}+c e^{x}\right) \\ &\frac{d^{3} y}{d x^{3}}=7\left(\frac{d y}{d x}\right)-6 y \\ &\frac{d^{3} y}{d x^{3}}-7\left(\frac{d y}{d x}\right)+6 y=0 \end{aligned}

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