solve dy/dx=y(2x+3)?

Question

Can anyone solve this when y=1

Answer 1

1/y dy = 2x+3 dx
∫1/y dy = ∫2x+3 dx
ln y = x²+3x+C

y=Ce^(x²+3x)

Unfortunatelly, your initial value is underdefined, since you don't tell us as what x-value y=1. If you mean y(0)=1, then:

1=Ce^(0)
C=1
y=e^(x²+3x)

Answer 2

dy/dx=y(2x+3)

dy/y=(2x+3)dx

integrate both sides

lny= x^2+3x+C

>>>> y= e^C.e^(x^2+3x) =Ke^(x^2+3x)

where K and C are constants

we are only told y=1 and not a
corresponding value for x,so the value
of K cannot be found

i hope that this helps

Answer 3

The equation can be written as
dy/y=(2x+3)dx
integrating both sides we get
ln(y)=x^2+3x or y=e^(x^2+3x)
now putting y=1 we get x=0,-3
Hence, proved

Answer 4

permit's simplify each little thing. :) permit's first open the brackets and simplify. So, we've, 2x = 5 + 12x - 15 = -10 + 12x be conscious: basically "3" is superior to "(4x-5)" and not "5+3". including "10" to the two the climate, we've, 2x + 10 = 12x Subtracting "2x" from the two the climate, we've, 10 = 10x Dividing "10" by skill of the two the climate, we've, a million = x that's comparable to x = a million desire that helped :)