Question

(X^2 y+y^3)dx-x^3 dy=0

Answer #1

Solve: 1.dy/dx=(e^(y-x)).secy.(1+x^2),y(0)=0.
2.dy/dx=(1-x-y)/(x+y),y(0)=2 .

Solve:
(2x^2 - y) dx + (x + y^2) dy = 0

solve for y:
1. dy/dx= xe^y separable
2. x(dy/dx)+3y=x^2 when y(5)=0 1st order linear

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

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

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

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy =
0. (a) Verify this is an exact equation
(b) Solve the equation

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

(x-y)dx + (y+x)dy =0 Solve the differential equation

Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy
(integral from 0 to 2)(integral from y/2 to 1) for cos(x^2) dx
dy

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