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Differential Equations
Solve the initial value problem :
d²x/dt² -6dx/dt + 9x = 0 , x(0) =6 ,x(0) = -1 .
d²x/dt² -6dx/dt + 9x = 0 , x(0) =6 ,x(0) = -1 .
Differential Equations
1. a) Solve the following ordinary differential equations:
i) dy/dx + 4xy = x
ii) d²y/dx² + 4dy/dx - 12y = cos2x .
i) dy/dx + 4xy = x
ii) d²y/dx² + 4dy/dx - 12y = cos2x .
Differential Equations
Solve:(i)(dy/dx-1)^2(d^2y/dx^2+1)^2y=sin^2(x/2)+e^x+x
(ii)2x^2y(d2y/dx2)+4y^2=x^2(dy/dx)^2+2xy(dy/dx)
(ii)2x^2y(d2y/dx2)+4y^2=x^2(dy/dx)^2+2xy(dy/dx)
Differential Equations
the normal form of the differential equation y"-xy'+(4x^2-1)y=?
Differential Equations
The differential equation of a damped vibrating system under the action of an external periodic force is: d^2x/dt^2 +2 m0 dx/dt +n^2x = a cos pt Show that, if n>m0>0 the complementary function of the differential equation represents vibrations which are soon damped out. Find the particular integral in terms of periodic functions
Differential Equations
Reduce the following PDE to a set of three ODEs by the method of separation of variables. d^2u/dr^2 +(2/r)(du/dr)+(1/r^2)(d^2u/dθ ^2) +(cot θ/r^2)(du/dθ) + (1/r^2 sin^2 θ)(d^2u/d φ^2) =0
Differential Equations
Solve the given differential equation by using appropriate substitution.
dy/dx = (1-x-y) / (x+y)
dy/dx = (1-x-y) / (x+y)
Differential Equations
solve the given initial value problem. Give the largest interval I over which the solution is defined.
(1+t^2)dy/dx + x = tan^-1 t , x(0) = 4
[Hint: In your solution let u = tan^-1 t ]
(1+t^2)dy/dx + x = tan^-1 t , x(0) = 4
[Hint: In your solution let u = tan^-1 t ]
Differential Equations
Solve the given differential equation by separation of variables.
(e^x + e^-x)dy/dx=y^2
(e^x + e^-x)dy/dx=y^2
Differential Equations
determine a region of the xy-plane for which the given DE would have a unique solution whose graph passes through a point (x0,y0) in the region
(y-x)y'=y+x
(y-x)y'=y+x
