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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 11 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 21 Differential Equations Exercise Revision Exercise Question 11 Maths Textbook Solution.

Answers (1)

Answer: xy^{11}+2y^{1}-xy+x^{2}-2=0

Hint: Find first and second derivative of equation put in given differential equation to verify.

Given: x y=a e^{x}+b e^{-x}+x^{2}, \quad x \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-x y+x^{2}-2 x

Solution:x y=a e^{x}+b e^{-x}+x^{2},

\mathrm{y}+\mathrm{x} \frac{\mathrm{d} \mathrm{y}}{\mathrm{dx}}=\mathrm{ae}^{\mathrm{x}}-\mathrm{be}^{-\mathrm{x}}+2 \mathrm{x} \ldots \text { differentiating using product rule }

\frac{\mathrm{dy}}{\mathrm{d} \mathrm{x}}+\mathrm{x} \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}+\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{ae}^{\mathrm{x}}+\mathrm{be}^{-\mathrm{x}}+2 \ldots \text { differentiating again } w . r \cdot t \text { to } x \\

\mathrm{xy}^{{}''}+2 \mathrm{y}^{{}'}-2=\mathrm{ae}^{\mathrm{x}}+\mathrm{be}^{-\mathrm{x}} \\                            

\mathrm{xy}^{{}''}+2 \mathrm{y}^{{}'}-2=\mathrm{x} \mathrm{y}-\mathrm{x}^{2} \\                                                \left[\begin{array}{l} x y=a e^{x}+b e^{-x}+x^{2} \\ x y-x^{2}=a e^{x}+b e^{-x} \end{array}\right]

\mathrm{xy}^{{}''}+2 \mathrm{y}^{{}'}-\mathrm{x} \mathrm{y}+\mathrm{x}^{2}-2=0

Hence proved

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