Differential Equations Answers

Find the general solution of the differential eq. y^2/2+2ye^t+(y+e^t)dy/dt=0

Find the orthagonal trijectries of the family of parabolas x=cy^2 and sketch their graph

If f and g are arbitrary function of their respective arguments, show that u= f( x -vt+i alpha y ) is a solution of (d^2u/dx^2 ) + (d^2u/dy^2) = (1/c^2) (d^2u/dt^2), where (alpha)^2 = 1-(v^2/c^2)?

A mass m , free to move along a line is attracted towards a given point on the line with a force proportional to its distance from the given point.If the mass starts from rest at a distance x_o from the given point, show that the mass moves in a simple harmonic motion?

Solve the differential equation d^2 y/dx^2 = a+bx+cx^2, given that dy/dx=0 and y= d, when x=0?

Obtain the Riccati equation associated with the equation y"+w^2 y=0 and hence find its solution?

Find the equation of the curve which passes through the point (1 , 4) and is such that : dy÷dx =2x^2 +3x +2

An advertising agent goes on vacation to 3 countries, India, New Zealand and Australia. He spends three times the number of days in New Zealand than he does in Australia and five days longer in India than in Australia. If his total vacation duration is 40 days, how many days did he spend in Australia

solve differential (y^2+yz)dx+(xz+z^2)dy+(y^2-xy)dz=0 please sir tell name of the form of which differential equation.and explain

Solve the initial value problem y"+3y'=0; y(0)=3, y'(0)=6