Differential Equations Answers

(y^2-2xy)dx-(2xy-x^2)dy=0

Solve
2x^2(∂^2/∂x^2) - 5xy[∂^2z/(∂x.∂y)] + 2y^2(∂^2z/∂y^2) + 2[x(∂z/∂x)+y(∂z/∂y) = 0

The initial value problem
dy/dx = 3y^2/3, y(0)=0, may not have unique solution in R(|x| < 1,|y| < 1 ).
True or false with correct explanation

Find a homogeneous linear differential equation with constant coefficients that's satisfied by x[e^-x(sin2x) + 3e^-x(cos2x)].

Show that if n>r>0, the complementary function represents vibrations which are ultimately damped out. Further, prove that the particular integral is of the form bcos(pt-α), where b^2= a^2/[(n^2-p^2)^2 +4r^2p^2].

The differential equation
(1-x^2)(∂^2z/∂x^2 -2xy[∂^2z/(∂x.∂y)] + (1-y^2)(∂^2z/∂y^2) + 2(∂z/∂x) +3y(∂z/∂y)=0, is elliptic for (x,y) outside the circle x^2 + y^2=1
True or false with correct explanation

The differential equation of damped vibrating system under the action of an external periodic force is d^2x/dt^2+ 2r(dx/dt)+ n^2x= acospt

y"+(y') ^2=2e^-y find the general solution

y"+2y'+y=3e^-x√x+1 find the general solution