Differential Equation First Order Linear

[ruiwp13]

Homework Statement

Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy

Homework Equations

y'+P(x)*y=Q(x)

The Attempt at a Solution

I tried to modify the equation to match the first order linear one, and I got:

e^(x^2)*dy/dx=x/y+x (divided everything by y),

but now I get:

dy/dx-x*1/y=e^(-x^2)*x

so instead of the normal form, I have now y'-P(x)*1/y = Q(x).

Did I do something wrong or missing something?

Thanks in advance

 

[Dick]

Homework Statement

Solve the following differential equation: y*e^(x^2)*dy/dx=x+xy

Homework Equations

y'+P(x)*y=Q(x)

The Attempt at a Solution

I tried to modify the equation to match the first order linear one, and I got:

e^(x^2)*dy/dx=x/y+x (divided everything by y),

but now I get:

dy/dx-x*1/y=e^(-x^2)*x

so instead of the normal form, I have now y'-P(x)*1/y = Q(x).

Did I do something wrong or missing something?

Thanks in advance

Why don't you just factor x+xy into x(1+y) and separate?

 

[ruiwp13]

Why don't you just factor x+xy into x(1+y) and separate?

∫y/(1+y) dy=∫e^(-x^2)*x dx

Like this?

 

[Dick]

∫y/(1+y) dy=∫e^(-x^2)*x dx

Like this?

Yes, like that.