Solve differential equation u′−5u=ve−5v
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dudv−5u=ve−5v dydx+Py=Q I.F.=e∫Pdx =e−∫5dv =e−5∫dv =e−5v u(I.F.)=∫ve−5v(I.F.)dv+c ue−5v=∫ve−5ve−5vdv+c ue−5v=∫ve−10vdv+c (1) Now find ∫ve−10vdv (by parts) =v∫e−10vdv−∫[ddv(v)∫e−10vdv]dv =ve−10v−10−∫[e−10v−10]dv =ve−10v−10+110e−10v−10 (2) from (1) and (2) ue−5v=ve−10v−10−1100e−10v+c u=(ve−10v−10e−5v)−1100e−10ve−5v+ce−5v u=ve−5v−10−1100e−5v+ce5v
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Find the Laplace transform L{u3(t)(t2−5t+6)} a)F(s)=e−3s(2s4−5s3+6s2) b)F(s)=e−3s(2s3−5s2+6s) c)F(s)=e−3s2+ss4 d)F(s)=e−3s2+ss3 e)F(s)=e−3s2−11s+30s2s3
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