1. The order and degree of the differential equation.
y +dy/dx =1/4∫ y .dx are-:
1. We have
dy/dx + dy/dx= 1/4 .∫ y.dx
⇒ dy/dx +d^2 y/dx^2 =1/4 y [on differentiating w.r.t. x ]
Differential equation is of order 2 and degree 1.
2. Example (x+1)dy/dx= 2xy {variable separable method}
We have, (x+1)dy=2xy dx
=>dy/y =2xy dx
=> ∫dy/y =2∫x/x+1 .dx
=> ∫1/y dy =2∫x+1-1/x+1 .dx
=> ∫1/y .dy =2∫|1-1/x+1 |.dx
=> log y =2[x – log|x+1|]+c
