Question

solve the ff. differential equations.

1. d^2/dx^2+ dy/dx=0
2.d/dx (x dy/dx+2y)= -2x^-3
3.2ydx+(x-x^3y^3)dy=0
4.(2y^2-6xy)dx+(3xy-4x^2)dy=0
5.(5x^2y+6x^3y^2+4xy^2)dx+(2x^3+3x^4y+3x^2y)dy=0

Answer 1

the first equation y'' + y = 0 is one the most fundamental differential equations there is. This is got to be in your text book or lecture notes. Look it up.

The next equation, first step is to integrate both sides wrt x. Then you have a separable equation.

Answer 2

1# http://www.wolframalpha.com/input/?i=%28d%5E2y%2Fdx%5E2%29%2B+dy%2Fdx%3D0

2# http://www.wolframalpha.com/input/?i=d%28x+dy%2Fdx%2B2y%29%2Fdx%3D+-2x%5E-3

3# ..

so on ... but i am not quite sure.