High number: the square of the general solution of differential equation YY "+ 1 = y ', the answer is y' = P, Y" = PDP / P, and only / P / > 1, / P / 1, / P/

If P = 0, i.e. y '= 0, then y "= 0 is substituted into the original equation, which obviously does not hold;
If P = 1 or - 1, i.e. y '= 1 or - 1, then y "= 0 is substituted into the original equation, which is obviously true,
Therefore, y = x + C or y = - x + C is also the solution of the original equation, where C is an arbitrary constant

Find the general solution of the differential equation YY ` ` + (y `) ^ 2 = y ',

yy''+(y')^2=(yy')'=y'
So YY '= y + C1, C1 is a constant
ydy/dx=y+c1
y/(y+c1)dy=dx
[1-c1/(y+c1)]dy=dx
y-c1ln(y+c1)=x+c
So the solution is x = y-c1 * ln (y + C1) + C, C, C1 is constant

What is the relationship between implicit function and differential

One way to find the implicit function is to use the invariance of the first-order differential form to differentiate both sides of the equation at the same time

General steps of implicit function differentiation

The independent variables and dependent variables are differentiated from the parameter variables respectively

Please ask an implicit function differential problem! Let Z ^ 3-3xyz = a ^ 3, find the quadratic partial derivative of Z / (partial derivative of X * partial derivative of Y)

/Is it a division or a mixed partial derivative of Z with respect to X and y? In my understanding, it should be the latter, right?
For the formula Z ^ 3-3xyz = a ^ 3, both sides first take the derivative about X, Z is regarded as a function of X and y, y and X are independent variables, and a should be a constant, right? After you find it out, just find the partial derivative of Y on both sides. Calculate it yourself. People can't calculate you well. Then you copy the answer, so you won't learn anything. You'll have to ask here next time you encounter a problem

Implicit function, differential method, expert Let x ^ 3 + y ^ 3 + Z ^ 3-3xyz = 0, determine the implicit function z = f (x, y), and find AZ / ax, AZ / ay

Let f (x, y, z) = x ^ 3 + y ^ 3 + Z ^ 3-3xyz
Fx'(x,y,z)=3x^2-3yz
Fy'(x,y,z)=3y^2-3xz
Fz'(x,y,z)=3z^2-3xy
∂z/∂x=-Fx'(x,y,z)/Fz'(x,y,z)=(yz-x^2)/(z^2-xy)
∂z/∂y=-Fy'(x,y,z)/Fz'(x,y,z)=(xz-y^2)/(z^2-xy)
This is the derivation formula of implicit function

High number: the square of the general solution of differential equation YY "+ 1 = y ', the answer is y' = P, Y" = PDP / P, and only / P / > 1, / P / 1, / P/