Question

I.F of $(1+x^3)\frac{dy}{dx}+3x^{2}y=si{n}^{2}x$:

• A. $1+x^3$
• B. $\frac{1}{1+x^3}$
• C. $3x^2$
• D. $\frac{1}{x^3}$

Answer 1

The correct option is A $1+x^3$

$\frac{dy}{dx}+\frac{3x^2}{1+x^3}y=\frac{{\sin }^{2}x}{1+x^3}$

$I.F=e^{\int P\left(x\right)dx}$

$=e^{\int \frac{3x^2}{1+x^3}}dx$

$=e^{log(1+x^3)}$

$\Rightarrow I.F=1+x^3$