Non homogeneous Differential Equation Assignment Help

Assignment Help: >> Solution of differential equation >> Non homogeneous Differential Equation

Non homogeneous Differential Equation:

Form 1363_Non homogeneous Differential Equation.png

Method: If 1627_Non homogeneous Differential Equation1.png,  put  x = X + h ,  y = Y + k such that a1h +b1k + c1 =  0,  a2h + b2k +c2 = 0 . In this way equation becomes homogeneous in X, Y. then use method for homogeneous equation.

If 1091_Non homogeneous Differential Equation2.pngThe equation in the form of variable which are separable in x, v.

Example : 1121_Non homogeneous Differential Equation3.png.

Solution:         Here  1655_Non homogeneous Differential Equation4.png

                        Thus we put  x- y = v

                          156_Non homogeneous Differential Equation5.png

                        or, 238_Non homogeneous Differential Equation6.png= dx or1754_Non homogeneous Differential Equation7.png Integrate 

                         2v + ln (v +2) = x + C, Put the  value of  v

                        ∴  x - 2y  + ln (x - y +2) = C

 

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