Differential Equations Answers

Solve the differential equations using integrating factor.

1. x dy/dx - y = x raise to power of 3 cosx, given that y=0 and x=π.

2. ( 1 + x square) dy/dx + 3xy = 5x given y=2 and x=1

Solve the differential equations using homogeneous equation.

1. ( 2y - x )dy/dx = 2x + y given that y=3 and x=2.

2. ( xy + y square) + ( x square - xy) dy/dx =0

Solve the differential equations using separating variables.

1. Cosy + ( 1+ e raise to power of -x ) siny dy/dx equal zero. Given that y= π/4 when x=0.

2. X raise to power of 2 ( y +1 ) + y raise to power of 2 ( x - 1 ) dy/dx equal zero.

(xz+yz)dz/dy + (xz-yz)dz/dy = x²+y² find the general solution

. Solve 𝑥 2 𝑑 2𝑦 𝑑2𝑥 − 2 𝑑𝑦 𝑑𝑥 − 4𝑦 = 0 

x-2)dx+4(x+y-1)dy=0

Verify that the total differential equation(1+yz)dx+x(z-x)dy-(1+xy)dz=0 is integrable and hence find its integral.

Verify that the total differential equation(1+yz)dx+z(z-x)dy-(1+xy)dz=0 is integrable and hence find its integral.

Verify that the total differential equation z(z-y)dx+z(x+z)dy+x(x+y)dz=0 is integrable and hence find its integral

x²U_xx-xyU_xy+y²U_yy-xU_x+yU_y=8y/x (x≠0,y≠0) find the general solution.