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Showing posts with the label differential equations

method of separation of variable.

In this method, we assume that the dependent variable is the product of two functions, each of which involves only one of the independent variables. So two ordinary differential equation are formed.

Solve (D²-6D+9)y=e³^x

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Solve (D²+6)y=sin4x

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Solve (D²+2D+1)y=x

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Solve D²(D²+4)y=96x²

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Solve (D²+2D+2)y= sinhx

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solve dy/dx=(4x+y+1)²

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Solve (4x+y)²dx/dy=1

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solve dy/dx-ytan2x=0,y(0)=2

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Solution:-

Find the differential equation corresponding to y=ae³^x+be^x

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Solve (dy/dx)-y=xy⁵

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Solve (D²+2)y = x²e³^x.

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Solution:-

What is Jacobian ?

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Answer:- A determinant which is defined for a finite number of functions of the same number of variables and in which each row consists of the first partial derivatives of the same function with respect to each of the variables is called Jacobian. e.g Jacobian of (u,v)/(x,y) is

Solve, xlogxdy/dx + y =2logx.

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Answer:-

Solve the equation y"'-2y"+y'=0.

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Answer:-

Find general solution of axy'=by.

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Answer:-

Solve, (x+2y)(dx-dy)=dx+dy.

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Answer:-

Solve, (2xy+e^y)dx+(x²+xe^y)dy.

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Solution:-

Solve, xdy/dx +2y =x²logx.

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Answer:-

Solve, (D⁴-3D²-4)y=5sin2x-e^-2x.

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Answer:-