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  • Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.3 question 10

Provide solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.3 question 10

Answers (1)

Answer:

y=a x^{3}+b x^{2}+c  is a solution

Hint:

Differentiate the given solution.

Given:

y=a x^{3}+b x^{2}+c


Solution:

Differentiating on both sides with respect to x

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left(a x^{3}+b x^{2}+c\right) \\\\ &\frac{d y}{d x}=3 a x^{2}+2 b x+0 \\\\ &\frac{d y}{d x}=3 a x^{2}+2 b x \end{aligned}        .................(i)

Differentiate equation (i) with respect to x,

\begin{aligned} &\frac{d^{2} y}{d x^{2}}=\frac{d}{d x}\left(3 a x^{2}+2 b x\right) \\\\ &\frac{d^{2} y}{d x^{2}}=6 a x+2 b \end{aligned}                ..............(ii)

Differentiate equation (ii) with respect to x,

\frac{d^{3} y}{d x^{3}}=6 a

Thus, y=a x^{3}+b x^{2}+c  is a solution of differential equation.

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