differential equations solve
(1+2x2)y’=x√(1+2x2)+8xy
x2 is square of x

Question

differential equations solve
(1+2x2)y’=x√(1+2x2)+8xy
x2 is square of x

eyust707 · Answer

I believe this can be solved with an integrating factor

eyust707 · Answer

play around with it for a sec and you get:

y'- (8x/1+2x2) y = x/sqrt(1+2x2)

eyust707 · Answer

which is the standard form for the integrating factor technique

eyust707 · Answer

eyust707 · Answer

wow they make that so confusing haha

eyust707 · Answer

basically your integrating fator is e^intP(x) dx

eyust707 · Answer

you multiply that through your equation

eyust707 · Answer

you take the integral of both sides

eyust707 · Answer

the left side just becomes your integrating factor times y

eyust707 · Answer

the right side you have to take an integral

eyust707 · Answer

solve for y and you end up with a general solution in terms of x and a constant

experimentx · Answer