Differential Equations Answers

Solve the following ordinary differential equations:

d²y/dx²+dy/dx+y=0

Find general solution of x(z^2-y^2)p+y(x^2-z^2)q=z(y^2-x^2)

1. (x+3y-5)dx-(x-y-1)dy=0

Find the general integral of

2x(y+z²)p+y(2y+z²)q=z²

Reduce the equation into canonical form and find the solution

sin²x u_xx+2cosx u_xy - u_yy=0

Reduce the equation into canonical form and find the solution

xu_xx +2(xy)^1/2 u_xy +yu_yy -u_x =0

Find the integral surface passing through the data curve x=1, z=y²+y of the equation x³ z_x+y(3x²+y)z_y =z(2x²+y)

Find the integral surface passing through the initial data curve C: x₀= -1, y₀= s, z₀= (s)^1/2 of the equation (x+2)p +2yq =2z

Find the solution of the equation

z=1/2(z_x² + z_y²) +(z_x -x)(z_y-y)

which passes through x- axis

Complete integral of pq=xy