If (dy/dx)+(y/x)=x2, then 2y(2)-y(1)=

Question

If (dy/dx)+(y/x)=x2, then 2y(2)-y(1)= (A) (9/4) (B) (11/4) (C) (13/4) (D) (15/4)

Tardigrade Admin · Accepted Answer

It is linear differential equation with I.F.= textexp ∫ (dx/x)=x ∴ Solution is, xy=∫ x2 xdx=(x4/4)+c Now, x=2 ⇒ 2y(2)=(16/4)+c and x=1 ⇒ y(1)=(1/4)+c ⇒ 2y(2)-y(1)=(15/4).

Q. If $\frac{d y}{d x} + \frac{y}{x} = x^{2}$ , then $2 y (2) - y (1) =$

$\frac{9}{4}$

$\frac{11}{4}$

$\frac{13}{4}$

$\frac{15}{4}$

It is linear differential equation with
$I . F . = exp \int \frac{d x}{x} = x$
$∴$ Solution is, $x y = \int x^{2} x d x = \frac{x ^{4}}{4} + c$
Now, $x = 2$
$\Rightarrow 2 y (2) = \frac{16}{4} + c$
and $x = 1$
$\Rightarrow y (1) = \frac{1}{4} + c$
$\Rightarrow 2 y (2) - y (1) = \frac{15}{4}$ .

Q. If dxdy​+xy​=x2, then 2y(2)−y(1)=

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