Question

integration ( y^2-x^2)/ (x^2 +y^2)^2 dx + (-2xy) / (x^2 +y^2)^2 dy

please give all detailed steps

Answer #1

**Since the order of both numerator and denominator on
right hand side is equal to 2, hence we need to use the
substitution**

**Integrating both sides we get**

**now substituting v=y/x in the equation to get the final
answer**

**Note - Post any doubts/queries in comments
section.**

Homogeneous Differential Equations:
dy/dx = xy/x^(2) - y^(2)
dy/dx = x^2 + y^2 / 2xy

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

(2xy+x^2+3y^2)dy/dx+(y^2+2xy+3x^2)=0

exact differential equation, (2xy+x)dx+(x^2+y)dy=0

Solve (2xy/x^2+1-2x)dx-(2-ln(x^2+1))dy=0, y(5)=0. Write the
solution in the explicit form. please explain steps Thanks!

method of separation of variables.(x2y+ 2xy+ 5y)dy=
(y2+ 7)dx2
integration factor. xdy/dx−2y=x4sinx3.
variation of parameters: y′−y=xex/x+1

solve ivp: (y+6x^2)dx + (xlnx-2xy)dy = 0, y(1)=2, x>0

Solve the following DE:
2xy^2 + 4 = 2(3 - x^2 y)dy/dx ; y(-1) = 8

Evaluate the integral by reversing the order of integration.
2
0
2
6ex/y dy dx
x

differential equations solve
(2xy+6x)dx+(x^2+4y^3)dy, y(0)=1

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