Differential Equations Answers

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)

Find the integral surface of the pde pq=z containing the curve x-0, z-y²

Obtain the complete integral xp^2- ypq + y^3q - y^2z= 0

(D^2+2D+5)y=xe^x

Solve:y``-3y`+2y=e²t;y(0)=3;y-1(0)=5 by laplace transform

x - 1 + Ce^-x

if from mean value theorem, f(x1)=f(b)-f(a)/b-a, then

solve (y-xz)p+(yz-x)q=(x+y)(x-y)

Show that y=x+tanx satisfies the differential equation cos²x d²y /dx² -2y+2x=0