Differential Equations Answers

Using charpits method

(p+q)(z-px-qy)=1

Solve Second Order (linear and homogenous) Differential Equation 𝑑²𝑦 /𝑑𝑥² + 𝑝(𝑥) 𝑑𝑦/ 𝑑𝑥 + 𝑄(𝑥)𝑦 = 0 by writing it in terms of quadratic equation and solving for its roots, mainly the complex roots. 

Solved by lagrange method

y^2 p^2+x^2q^2=x^2y^2z^2

xpq+yq^2=1 using charpits method

(p+q)(z-px-qy)=1

y''(x) - y'(x) + 2y(x) = 2e^x

(D^2 -4DD^'+ 3D^'^2)z =0

(y+x)p+(y-x)q=z

Find the integral surface for the differential equation z(xz_x-yz_y)=y²-x² passing through the initial data curve (2s, s, s)

Solve z_x+z_y = z² with the initial conditions z(x, 0)=f(x)