Differential Equations Answers

Find the complete integral of
p²+q²-2px-2qy+1 =0

Find the integral surface of the linear PDE
x(y²+z)p - y(x²+z)q = (x²-y²)z , which contains the straight line x+y =0 , z=1.

Find the differential equation of the family of surfaces ∅(x+y+z , x²+y²-z²) =0.
what is the order of this PDE ?

Verify that the equation 2(y+z)dx - (x+z)dy+ (2y-x+z)dz = 0 is integrable and find its primitive .

Solve:
(1+x)² d²y/dx² + (1+x) dy/dx + y = 4 cos ln(1+x)

Solve the IVP.
x² dy/dx = cosx - 2xy , y(π) = 0, x>0.

Solve.
d²y/dx² - 4x dy/dx + (4x²-1)y = -3exp(x²)sin(2x)

Solve the PDE.

x² d²z/dx² ⁻y² d²z/dy² + x dz/dx - y dz/dy = ln x

Find the general solution of the differential equation .
y²/2 + 2yexp(t) + (y+exp(t))dy/dt = 0

If y₁ = 2x+2 and y₂= -x²/2 are the solutions of the equation y= xy´+( y´)²/2 ,
Then are the constant multiples c₁y₁ and c₂y₂ , where c₁,c₂ are arbitary, also the solutions of the given DE ? Is the sum y₁+y₂ a solution ? Justify your answer .