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  • Need solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 21

Need solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 21

Answers (1)

Answer:

 The required differential equation is

y_{2}-4y_{1}+4y=0

Hint:

 Differentiating the given equation with respect to x

Given:

 y=e^{2x}(a+bx)

Solution:

y=e^{2x}(a+bx) \qquad \qquad \dots(i)

Differentiating with respect to x, we get

\begin{aligned} &y_{1}=e^{2x}(0+b)+(a+bx)e^{2x}.2 \\ &y_{1}=e^{2x}b+(a+bx)e^{2x}.2 \qquad \qquad \dots(ii) \end{aligned}

Putting (i) in (ii)

\begin{aligned} &y_{1}=be^{2x}+2y \\ &y_{1}=2y=be^{2x} \qquad \qquad \dots(iii) \end{aligned}

Again, Differentiating with respect to x, we get

\begin{aligned} &y_{2}-2y_{1}=be^{2x}.2 \qquad \qquad \dots(iv) \end{aligned}

Putting (iii) in (iv), we get

\begin{aligned} &y_{2}-2y_{1}=2y_{1}-4y \end{aligned}

 The required differential equation is

y_{2}-4y_{1}+4y=0

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Gurleen Kaur

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