Differential Equations Answers

Solve the following differential equations:
i) (x²+y²)dy/dx=xy

Solve the differential equation:
(z+z^3)cosxdx-(z+z^3)dy+(1-z^2)(y-sinx)dz=0

If f and g are arbitrary functions of their respective arguments, show that u=f(x-vt+iay)+g(x-vt+iay) is a solution of d2u/dx2+d2u/dy2=1/c^2 .d2u/dt2,where a^2=1-(v^2/c^2)

Using Jacobi’s method find the complete integral of the equation 2u1xz+3u2y^2+u2u3

If y1 = 2x + 2and y2 = −x^2/2 are the solutions of the equation y = x y′+(y')^2/ 2then are the constant multiples c1y1and c2y2 , where c1, c2 are arbitrary, also the solutions of the given de? is the sum y1+ y2 a solution? Justify your answer.

Find the general solution of the differential equation y^2lny=xpy+p^2, Does the equation has any singular solution? If yes ,obtain it.

Solve the following boundary value problem
Ut=Uxx,0<x<l,t>0
U(0,t)=U(l,t)=0
U(x,0)=x(l-x),0<=x<=1

solve the second order differential equation
d
2
y
d
x
2
−
4
y
=
12
x
,
y
(
0
)
=
4
,
y
′
(
0
)
=
1
d^2y/dx^2−4y=12x,y(0)=4,y′(0)=1

obtain the riccati equation associated with the equation y''+w2y=0 and hence find its solution.

w=omega

Solve the differential equation d2y/dx2=a+bx+cx2 given that dy/dx=0 and y=d when x=0.