Question

The differential equation whose general solution is y= Ac^-x^2​

Answer 1

Answer:

17%

Solution:

Ax2+By2=1 can be written as

By2=1−Ax2

Differentiating w.r.t. ′x′, we get

2Bydydx=−2Ax

⇒dydx=−ABxy⇒−AB=yxdydx

Again differentiating w.r.t. ′x′, we get

d2ydx2=(−AB)(y−xdydxy2)

=(−AB)(y−x(−AB.xy)y2)

d2ydx2=(yx.dydx)y−x(yx.dydx.xy)y2

=yx.dydx(y−xdydxy2)

⇒y2d2ydx2=y2xdydx−y(dydx)2

⇒yd2ydx2+(dydx)2−yxdydx=0

⇒xyd2ydx2+x(dydx)2−ydydx=0

has 2nd order and first degree.

Step-by-step explanation:

I HOPE IT HELP YOU