The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x, t)-x+(-*-20)(x*+2) 4. Oc. u(x, t)-2x Od. 1 u(x, t) - x - - (e*-2)o**20) e. 1 u(x, t)=x+ (e

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Q: If f(x) = (x6 + 4x) ³, then df(x) a) 3(x64x)² (x5 + 4) b) 3(x6 +4x)² Oc) (x6 +4x)² (6x5) da equals…

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A: Take u(x,y)=x2+y2 We have  uxx(x,y)=2 and uyy(x,y)=2

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Q: Find: te (1 + Inx + ) he y? y+ylnx+ 2x O ylnx +y o 1 y x2 « Previous 98 %23 立

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Q: 1 If f(x,y,z)= of then x-y-3-

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A: Some of the proprieties of Laplace transform Lu(t-c)g(t)=e-2cL[g(t+c)] Ltneat=n!(s-a)n+1 Leat=1s-a

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

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Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.