Solve equation y ^ 2 + x ^ 2 * (dy / DX) = x * y * (dy / DX)

Solve equation y ^ 2 + x ^ 2 * (dy / DX) = x * y * (dy / DX)

Dy / DX = y ^ 2 / (xy-x ^ 2) = (Y / x) ^ 2 / (Y / x-1), let u = Y / x, then dy / DX = u + XDU / DX, and the equation becomes U + XDU / DX = u ^ 2 / (U-1). Next, you can complete it by yourself. Move u to the right and use the separation of variables method

Let the function x = x (y) be determined by the equation y ^ x + X + y = 4, then DX / dy|y = 1=

Let f (x, y) = y ^ x + X + y-4 = 0
The partial derivative of F (x, y) to X is: LNY * y ^ x + 1
The partial derivative of Y is: X * y ^ (x-1) + 1
dx/dy=[x*y^(x-1)+1/(lny*y^x+1)
By substituting y = 1 into the implicit function f (x, y), x = 3 can be obtained
So DX / dy = (3 + 1) / 1 = 4

On May 15, 2009, how to use matlab to solve the differential equation d ^ y / D (x) ^ 2 + 2 * dy / DX + 2Y = 0 when y (0) = 1, y (0)=

y = dsolve('(Dy)^2 + y^2 = 1','y(0) = 0')
y =
-Sin (T) or sin (T)
Both can

Differential equation d ^ 2Y / dt ^ 2-dy / dt + y = 1, Y0 = 0, Y1 = 0. How to solve it with MATLAB

There is a problem with the writing format. A comma is missing
dsolve('D2y-Dy+y=1','y(0)=0','y(1)=0')
ans =
exp(1/2*t)*sin(1/2*3^(1/2)*t)*(-1+cos(1/2*3^(1/2))*cosh(1/2)+cos(1/2*3^(1/2))*sinh(1/2))/sin(1/2*3^(1/2))/(cosh(1/2)+sinh(1/2))-exp(1/2*t)*cos(1/2*3^(1/2)*t)+1

Solving differential equation dy / dx-2y / (x + 1) = (x + 1) ^ 5 / 2 with MATLAB

dsolve('Dy-2*y/(x+1)=(x+1)^5/2')
ans =
(C2*exp((2*t)/(x + 1)))/4 - (3*x)/2 - (15*x^2)/4 - 5*x^3 - (15*x^4)/4 - (3*x^5)/2 - x^6/4 - 1/4

Matlab solution of differential equations DX / dt = x + y dy / dt = X-Y

I don't know if the solution is right
Procedure:
dsolve('Dx=x+y','Dy=x-y','t')
The solution is: x = C1 * exp (2 ^ (1 / 2) * t) + C2 * exp (- 2 ^ (1 / 2) * t)
y=C1*2^(1/2)*exp(2^(1/2)*t)-C2*2^(1/2)*exp(-2^(1/2)*t)-C1*exp(2^(1/2)*t)-C2*exp(-2^(1/2)*t)