Differential Equations Answers

The differential equation
(y.lnx-1)ydx=xdy is a linear differential equation of first order and first degree.
True or false with full explanation

Solve the partial differential equation: x^2p+y^2q=z^2

Solve the following differential equation by reducing it to normal form using change of dependent variable
d^2y/dx^2-2xdy/dx + (x^2+2)y= e^1/2(x^2+2x)

Solve for the equation of the orthogonal trajectory: 1. Y = 3x - 1 + Ce-3x

Show whether the differential equation given below is linear or nonlinear.
Also determine its order:
dR/dt=-k/R^n
Where n=1

(x^2D^2-3xD + 1)y= x^-1 [1 + logx sin (logx)]

2D^2-D'^2+D=x^2-y

(√(1-y^2)dx)-(√(1-x^2)dy)=0, y(0)=√3/2)

Solve by jacobi 's method
1) (p^2+q^2)y= qz
2)p= (z+qy)^2
3)z^3 = pqxy
4) (q-px-p^2)=0