Chapter 9: Differential Equations

We know that, the equation of all non-vertical lines are y = mx + c

On differentiating w.r.t. x, we get

dy/dx = m

Again, on differentiating w.r.t. x, we have

d²y/dx² = 0

Thus, the required equation is d²y/dx² = 0.

Given differential equation,

dy/dx + 2xy = y

Given equation, dy/dx + ay = e^mx

Solving for linear differential equation of first order, we have

P = a and Q = e^mx

Given differential equation, dy/dx + 1 = e^x+y

Substituting x + y = t and differentiating w.r.t. x, we have

Given equation, ydx – xdy = x²ydx

y dx – x²y dx = xdy

y (1 – x²) dx = xdy

Given equation, dy/dx = 1 + x + y² + xy²