Question

I.F of $(x^3+5)\frac{dy}{dx}+3x^{2}y={\cos }^{2}x$ is:

• A. $e^{5+x^3}$
• B. $5+x^3$
• C. $log(5+x^3)$
• D. $\frac{3x^2}{5+x^3}$

Answer 1

Answer: (B)

$5+x^3$

$y^1+\frac{3x^{2}y}{x^3+5}=\frac{cos{}^{2}x}{x^3+5}$

$P\left(x\right)=\frac{3x{}^2}{x^3+5}[t=x^3+5]$

$\int P\left(n\right)dn=\int \frac{3x{}^2}{x^3+5}dn=\int \frac{dt}{t}=log\left(t\right)=log(x^3+5)$

$I.F=e^{\int P\left(n\right)dn}=e^{log(x^3+5)}=x^3+5$