Differential Equations Answers

Solve : 2(2y^2+yz -z^2)dx+x(4y+z)dy+x(y-2z)dz= 0

find the integral curves of the equation dx/xz-y=dy yz-x=dz/xy-z

Solve 2(2y^2+yz -z^2)dx+x(4y +z)dy+x(y -2z)dz= 0

D2y/dx2-24dy/dx+144=0

Solve (D^2 -4D+3)y = e^x cos 2x + cos3x 

Find the partial differential equation whose general solution is given by the arbitrary

function F(2x + 3y + 4z , x^2 + y^2 − 2) = 0

Find a solution of the Bessel’s equation of order zero. 

5. Find the series solutions of the Laguerre equation (1 ) 0

2

x y   x y  ny  of the form 

( ) ( ) 0 y x c L x  n

, where 

r r

n

r

n x

n r r

n

L x

2

0 ( )![( )!]

( )! ( ) ( 1)



  



. Hence find first four polynomials.

cotxdy=ydx=(cotx)(3e^sinx)dx

Solve [2y^2 – 4x + 5]dx = [y – 2y^2 - 4xy]dy