Question

Given the differential equation
$\frac{dy}{dx}=\frac{6x^{2}}{2y+cos\,y}; y\left(1\right)=\pi$.
Mark out the correct statement.

• A. solution is $y^2 - sin\, y = - 2x^3 + C$
• B. solution is $y^2 + sin\, y = 2x^3 + C$
• C. $C=\pi^{2}+2\sqrt{2}$
• D. $C=\pi^{2}+2$

Answer 1

Answer: (B)

We have, $\int \left(2y+cos\,y\right)dy=\int 6x^{2}\,dx$
$\Rightarrow y^{2}+sin\,y=2x^{3}+C$
$\because y\left(1\right)=\pi$
$\Rightarrow C=\pi^{2}-2$
$\therefore $ Solution is $y^{2}+sin\,y=2x^{3}+\pi^{2}-2$
$\Rightarrow y^{2}+siny=2x^{3}+C$, where $C=\pi^{2}-2$