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  • Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 32 maths

Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 32 maths

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of exponential sin and cos functions

Given:

y=e^{x}(\sin x+\cos x), \text { show } \frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0

Solution:

y=e^{x}(\sin x+\cos x)

        \begin{aligned} &\text { Differentiate the equation w.r.t } x\\ &\frac{d y}{d x}=e^{x}(\cos x-\sin x)+e^{x}(\sin x+\cos x)\\ &\frac{d y}{d x}=e^{x}(\cos x-\sin x)+y \end{aligned}

        \begin{aligned} &\text { Differentiate again }\\ &\frac{d^{2} y}{d x^{2}}=e^{x}(-\sin x-\cos x)+e^{x}(\cos x-\sin x)+\frac{d y}{d x}\\ &\frac{d^{2} y}{d x^{2}}=-y+\frac{d y}{d x}-y+\frac{d y}{d x}\\ &\therefore \frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}+2 y=0 \end{aligned}

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Gurleen Kaur

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