Differential Equations Answers

solve the following differential equations
1- (y-2)dx-(x-y-1)dy=0
2- (x-4y-9)dx+(4x+y-2)dy=0

Find the complete integral using Charpit Method : 2x(q²z²+1) = pz

d^2y/d^2 = 1/x(x+1) + cosec^2x

Find T(x,t) in a laterally insulated 2 m-long rod if k=10-4 m2/s and T(x,0)=100(2x-x2), T(0,t)=0=T(2,t).

Compute the n-th differential coefficient of \\(y=x\\log_{e}x\\)\n

by Charpits AE sobylve z=p^2x+q^2y

consider the system:
dx/dt = x^2+y
dy/dt = x^2*y^2
Show that, for the solution (x(t),y(t)) with initial ocndition (x(0),y(0)) = (0,1), there is a time t* such that x(t)--> infinity as t--> t*. In other words the solutions blows up in finite time.

Solve the differential equation y'=x(1+y^2)

If (y=2x+ce^x) is a solution of the differential equation frac {dy}{dx}-y=2(1-x) then find the particular solution satisfied by x=0, y=3

Obtain the solution for the initial value problem y'+(cotx)y=xcscx, y left frac{pi}{2} right=1