Find the differential equation associated with the following function

Question

anonymous · Answer

$$y*x = b*e ^{x+2a} + a *x ^{2}$$  
(e= neperian ; a & b constants)

amistre64 · Answer

i do not see any derivatives of y in there

are you trying to determine its derivatives perhaps?

amistre64 · Answer

$$yx = b~e ^{x+2a} + a ~x ^{2}$$
$$D[yx] = D[b~e ^{x+2a}] +D[ a ~x ^{2}]$$
$$y'x+yx' = b~D[e ^{x+2a}] +a~D[x ^{2}]$$
$$y'x+yx' = b~(x')e ^{x+2a} +2ax~x'$$assuming the we derive with respect to x, then x'=dx/dx=1
$$y'x+y = b~e ^{x+2a} +2ax$$
$$y'+\frac1xy = \frac bx~e ^{x+2a} +2a$$

anonymous · Answer

Wrong, the constants must disapear whe you find the derivatives

amistre64 · Answer

not in general no

the derivative of 2x^3 is 2*3x^2

amistre64 · Answer

the derivative if 5e^(2x) is:  5*2e^(2x)

amistre64 · Answer

the only time a constant "disappears" ina derivative is when you are taking the derivative of a constant.

the derivative of 4 is:  0