Solution of the differential equation (dy/dx)+(y/x)=sinx is

Question

Solution of the differential equation (dy/dx)+(y/x)=sinx is (A) x(y + cos x) = sin x + c (B) x(y - cos x) = sin x + c (C) xy cos x = sin x + c (D) x(y + cos x) = cos x + c

Tardigrade Admin · Accepted Answer

(dy/dx)+(y/x)=sinx It is linear differential equation with I.F.=e∫ (1/x)dx=elogx=x Now, solution is y⋅ x=∫ x sinx dx+c ⇒ x⋅ y=-xcosx+sinx+c ⇒ x(y+cosx)=sinx+c

Q. Solution of the differential equation $\frac{d y}{d x} + \frac{y}{x} = s in x$ is

$x (y + cos x) = s in x + c$

$x (y - cos x) = s in x + c$

$x y cos x = s in x + c$

$x (y + cos x) = cos x + c$

$\frac{d y}{d x} + \frac{y}{x} = s in x$
It is linear differential equation with
$I . F . = e^{\int \frac{1}{x} d x} = e^{l o gx} = x$
Now, solution is $y \cdot x = \int x s in x d x + c$
$\Rightarrow x \cdot y = - x cos x + s in x + c$
$\Rightarrow x (y + cos x) = s in x + c$

Q. Solution of the differential equation dxdy​+xy​=sinx is

x(y+cosx)=sinx+c

x(y−cosx)=sinx+c

xycosx=sinx+c

x(y+cosx)=cosx+c