Question

If the equation is non homogeneous, differential equation is the solution exist?

Answer 1

The simple answer is that it often does, because the inhomogeneous DE can be split into a homogeneous part solvable by conventional means (e.g., solving the characteristic equation), and a particular solution by examining what remains when the homogeneous part is removed (and solved).

Comments

x2+y'=4x2+7xy+2y2

 

i let: y=ax ; dy= adx + xda

then substitute,

 

x2 (adx + xda) = 4x2 + 7x(ax) +2(ax)2

adx + xda = 4 + 7a + 2a2

∫dx/x + ∫da/a + (2a-7)/x = 4/ax

ln x + ln a + ???????????

cant answer next procedure