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  • Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 23

Need solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 23

Answers (1)

Answer: y+1=2 e^{\frac{x^{2}}{2}}

Given: slope =x+y x

Hint: x-coordinate is abscissa and y-coordinate is ordinate

Solution:

According to ques,

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

Integrating both sides w.r.t x

        \int \frac{d y}{1+y}=\int x d x

        \log |1+y|=\frac{x^{2}}{2}+c \quad \text {........(i) } \quad\left[\int \frac{d x}{x}=\log x+c\right]

Since, the curve passes through (0,1)

        \begin{aligned} &\log |1+1|=\frac{0^{2}}{2}+c \\\\ &\mathrm{c}=\log 2 \end{aligned}

Putting the value of c in eqn (i)

        \begin{aligned} &\log |1+y|=\frac{x^{2}}{2}+\log 2 \\\\ &\log |1+y|-\log 2=\frac{x^{2}}{2} \quad\quad\quad\quad\left[\log m-\log n=\log _{n}^{m}\right] \end{aligned}

        \begin{gathered} \log \frac{1+y}{2}=\frac{x^{2}}{2} \\\\ \frac{1+y}{2}=e^{\frac{x^{2}}{2}} \\\\ y+1=2 e^{\frac{x^{2}}{2}} \end{gathered}

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