solving differential equations help

[engr_joni_ee]

I need help in solving differential equations

1- xy' - y = x^2

2- y' -y/x = x sinx
 
3- y' -3x^2 y = (4 x e ^(x^3))/sqrt(1+(x^2))

4- y'-y/x = x cos x

 

[wwfeldman]

they are all first order linear ordinary differential equations
there are a variety of methods used, which may be found on the internet

you can check the answers with wolfram alpha:
go to the wolfram alpha website and type something like find y for xy' - y = x^2
enter and wait. it will give you the solution but won't tell you how to do it.

 

[_Eduardo_]

I need help in solving differential equations

1- xy' - y = x^2

2- y' -y/x = x sinx
 
3- y' -3x^2 y = (4 x e ^(x^3))/sqrt(1+(x^2))

4- y'-y/x = x cos x

Hint:

xy' - y = x^2 (y/x)'

and

y' -3x^2 y = (y e^(-x^3))' e^(x^3)

Then

1- x^2 (y/x)' = x^2  -----> solve  (y/x)' = 1

2- x (y/x)' = x sinx   -----> solve  (y/x)' = sinx

3- (y e^(-x^3))' e^(x^3) = (4 x e ^(x^3))/sqrt(1+(x^2)) -----> solve  (y e^(-x^3))' = (4 x)/sqrt(1+(x^2))
 
4- x (y/x)' = x cosx  -----> solve  (y/x)' = cosx

All are easy to integrate.