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Show that the Integrating factor of the equation (x^2+y^2+2x)dx + 2ydy=0 is e^x and its particular solution is x^2 + y^2=2e^1-x when x=y=1
Solve: (3ydx - 2xdy) + x^2y^-1(10ydx - 6xdy)=0
Solve: 2siny^2dx + xycos^2dy=0 ,
Given: y(2)=√π/2
State and prove existence and uniqueness theorem
find the integral surface of the equation : (x-y)y^2p + (y- x)x^2q=(x^2 + y^2)z,
through the curve xz =a^2, y = 0

Solve the equations

dx/x+y-z=dy/y+z-x=dz/z+x-y



What is the degree and the order of this equation
y”y-(y’)^2=2

d^2y/dx^2 + 2dy/dx * d^3y/dx^3 +x=0
What is the degree and the order of y’-y^7=0
State and prove existence and uniqueness theorem.

Define Index of a stationary point with example. 


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