Given the differential equation (dy/dx)=(6x2/2y+cos y); y(1)=π. Mark out the correct statement.

Question

Given the differential equation (dy/dx)=(6x2/2y+cos y); y(1)=π. Mark out the correct statement. (A) solution is y2 - sin y = - 2x3 + C (B) solution is y2 + sin y = 2x3 + C (C) C=π2+2√2 (D) C=π2+2

Tardigrade Admin · Accepted Answer

We have, ∫ (2y+cos y)dy=∫ 6x2 dx ⇒ y2+sin y=2x3+C ∵ y(1)=π ⇒ C=π2-2 ∴ Solution is y2+sin y=2x3+π2-2 ⇒ y2+siny=2x3+C, where C=π2-2

Q. Given the differential equation
$\frac{d y}{d x} = \frac{6 x ^{2}}{2 y + cos y}; y (1) = π$ .
Mark out the correct statement.

solution is $y^{2} - s in y = - 2 x^{3} + C$

solution is $y^{2} + s in y = 2 x^{3} + C$

$C = π^{2} + 22$

$C = π^{2} + 2$

We have, $\int (2 y + cos y) d y = \int 6 x^{2} d x$
$\Rightarrow y^{2} + s in y = 2 x^{3} + C$
$∵ y (1) = π$
$\Rightarrow C = π^{2} - 2$
$∴$ Solution is $y^{2} + s in y = 2 x^{3} + π^{2} - 2$
$\Rightarrow y^{2} + s in y = 2 x^{3} + C$ , where $C = π^{2} - 2$

Q. Given the differential equation dxdy​=2y+cosy6x2​;y(1)=π. Mark out the correct statement.

solution is y2−siny=−2x3+C

solution is y2+siny=2x3+C

C=π2+22​

C=π2+2