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  • Need solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 16 textbook solution.

Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 16 textbook solution.

Answers (1)

Answer : (d) y=\tan \left(x+\frac{x^{2}}{2}\right)

Hint: Use variable separable method i.e.  take y terms in one side and x terms in the other.

Given :  \frac{d y}{d x}=1+x+y^{2}+x y^{2}, \quad y(0)=0

Explanation : \frac{d y}{d x}=1+x+y^{2}+x y^{2}

\begin{aligned} &\frac{d y}{d x}=1+x+y^{2}(1+x) \\ &\frac{d y}{d x}=(1+x)\left(1+y^{2}\right) \\ &\frac{d y}{1+y^{2}}=(1+x) d x \end{aligned}

\begin{aligned} &\tan ^{-1} y=x+\frac{x^{2}}{2}+C\\ &\text { Also we have } y(0)=0\\ &\tan ^{-1}(0)=0+\frac{0}{2}+C\\ &C=0 \end{aligned}

\begin{aligned} &\text { So, } \tan ^{-1} y=x+\frac{x^{2}}{2} \\ &y=\tan \left(x+\frac{x^{2}}{2}\right) \end{aligned}

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