Differential Equations Answers

Solve the following by Cauchy Euler differential Equation 4x^2 (d^2 y)/(dx^2 )-4x dy/dx+3y=sin⁡(ln(-x))            x<0

Equation 

x  y p  x  y q  z  z

2

cos( ) sin( )

is a quasi-linear equation

1. (x²-4xy-2y²)dx + (y²-4xy-2x²)dy=0
2. (x²-xtan²y+sec²y)dy = (tany-2xy-y)dx
3. (2xy⁴e^y+2xy³+y)dx + (x²y⁴e^y-x²y²-3x)dy=0
4. (y/x secy-tany)dx+(secy logx-x)dy=0
5. y dy/dx +4x/3 -y²/3x =0

If d²x/dt² + g(x-a)/b = 0, (a,b,g being positive constants) and x=a' ans dx/dt = 0 when t = 0, show that x = a + (a'-a) cos[(√g)t/b].

3) find the integral surface of the equation (y-z){2xyp+(x^2-y^2)q}+z(x^2-y^2)=0 through the curve x=t^2, y=0 , z=t^3

A solution of Initial Value Problem

(1-t²)(d²y/dt²) + 2t(dy/dt) - 2y = 0, y(0) = 3, y'(0) = -4

is y1=t. Use the method of reduction of order to find a general solution of Initial Value Problem on the interval -1<t<1.

2)solve (2x^2+2xy+2xz^2+1)dx+dy+2zdz=0

1)form a pde by eliminating the arbitrary function from z=exp(2x+3y)f(2x-3y)

solve dx/(y-z)=dy/(z-x)=dz/(x-y)

solve the undetermined coefficient y''+y=x