Differential Equations Answers

2(y+z)dx-(x+z)dy+(2y-x+z)dz=0

Solve the PDE ∂z/∂x + ∂z/∂y = z²

yp+x^2q^2=2x^2y

(1-x^2)yp^2+x^2q=0

ydy=4x(y^2+1)^1/2 dx y(0)=1

P^2+px+q=z

yp+xq+pq=0

(3x^2y^3e^x+y^3+y^2)DX+(x^2y^3e^x-xy)sy=0

A particle of mass m thrown vertically upward with velocity v0. The air resistance is mgcv² where c is a constant with v us the velocity at any time t. Show that the time taken by bthe particle to reach the highest point is given by v0 underroot c =tan(gt underroot c)

(x^2+y^2)p +2xyq=(x+y)z