Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations

Examples

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Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations: Examples

R.H.S = xr ys

Example 1.5.12: Solve [D2 - 7DD' + 6D '2] z = xy

Solution: Given: [D2 - 7DD' + 6D '2] z = xy

The auxiliary equation is



Example 1.5.13 : Solve [D2 + 3 DD' + 2D '2] z = x + y

Solution: Given: [D2 + 3DD' + 2D 2]z = x+y

The auxiliary equation is



Example 1.5.14: Solve [D2 + 4DD' - 5D'2] z ] z = x + y2+л

Solution : Given : [D2 + 4DD' − 5D'2]z = x + y2+π

The auxiliary equation is


 

EXERCISES

Find the particular Integral of



R.H.S = eax + by xr ys

Example 1.5.15 : Solve : [D2 - DD' - 6D'2] z = x2y + e3x+y.

Solution : Given : [D2 - DD' - 6D'2] z = x2y + e3x+y.

The auxiliary equation is



Example 1.5.16 : Solve (D2 + DD' - 6D2) z = x2y+e3x+y

Solution: The auxiliary equation is m2+m-6 = 0

m = 2, -3


Example 1.5.17: Solve (D2 - 6DD' + 5D 2) z = ex sinh y + xy

Solution : Given: [D2 – 6DD ' + 5D 2 ] = ex sinh y + xy


Example 1.5.18 : Solve (D2 + 2DD' + D'2) z = x2y+ ex-y

Solution :


Transforms And Partial Differential Equations: UNIT I: Partial Differential Equations : Tag: : - Examples

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MA3351 3rd semester civil, Mechanical Dept | 2021 Regulation | 3rd Semester Mechanical Dept 2021 Regulation