Uppgift 3.7: 1, 2, 3, 4. LC-krets. 

Typesetting:-mrow(Typesetting:-mi( 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`*`(L, `*`(diff(i(t), t))), `*`(R, `*`(i(t)))) = e(t) (6.1)
 

Uppgift 1 

Sätt in begynnelsedata, högerled och numeriska värden. 

Typesetting:-mrow(Typesetting:-mi( 

i(0) = 4 (6.2)
 

Typesetting:-mrow(Typesetting:-mi( 

{i(0) = 4, `+`(`*`(5, `*`(diff(i(t), t))), `*`(25, `*`(i(t)))) = 0} (6.3)
 

Typesetting:-mrow(Typesetting:-mi( 

i(t) = `+`(`*`(4, `*`(exp(`+`(`-`(`*`(5, `*`(t)))))))) (6.4)
 

Uppgift 2 

Typesetting:-mrow(Typesetting:-mi( 

i(0) = 0 (6.5)
 

Typesetting:-mrow(Typesetting:-mi( 

{i(0) = 0, `+`(`*`(5, `*`(diff(i(t), t))), `*`(25, `*`(i(t)))) = 100} (6.6)
 

Typesetting:-mrow(Typesetting:-mi( 

i(t) = `+`(4, `-`(`*`(4, `*`(exp(`+`(`-`(`*`(5, `*`(t))))))))) (6.7)
 

Typesetting:-mrow(Typesetting:-munder(Typesetting:-mo( 

4 (6.8)
 

Uppgift 3 

Typesetting:-mrow(Typesetting:-mi( 

{i(0) = 0, `+`(`*`(5, `*`(diff(i(t), t))), `*`(25, `*`(i(t)))) = `+`(`*`(100, `*`(cos(`+`(`*`(60, `*`(t)))))))} (6.9)
 

Typesetting:-mrow(Typesetting:-mi( 

i(t) = `+`(`*`(`/`(4, 145), `*`(cos(`+`(`*`(60, `*`(t)))))), `*`(`/`(48, 145), `*`(sin(`+`(`*`(60, `*`(t)))))), `-`(`*`(`/`(4, 145), `*`(exp(`+`(`-`(`*`(5, `*`(t))))))))) (6.10)
 

Typesetting:-mrow(Typesetting:-mi( 

Plot_2d
 

Uppgift 4 

Typesetting:-mrow(Typesetting:-mi( 

{`+`(`*`(2, `*`(diff(i(t), t))), `*`(40, `*`(i(t)))) = `+`(`*`(100, `*`(exp(`+`(`-`(`*`(10, `*`(t)))))))), i(0) = 0} (6.11)
 

Typesetting:-mrow(Typesetting:-mi( 

i(t) = `*`(`+`(`*`(5, `*`(exp(`+`(`*`(10, `*`(t)))))), `-`(5)), `*`(exp(`+`(`-`(`*`(20, `*`(t))))))) (6.12)
 

Typesetting:-mrow(Typesetting:-mi( 

proc (t) options operator, arrow; `*`(`+`(`*`(5, `*`(exp(`+`(`*`(10, `*`(t)))))), `-`(5)), `*`(exp(`+`(`-`(`*`(20, `*`(t))))))) end proc (6.13)
 

Typesetting:-mrow(Typesetting:-mi( 

Plot_2d
 

Maximum beräknas med standardmetoden frÃ¥n analys A. 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`*`(`/`(1, 10), `*`(ln(2)))) (6.14)
 

Typesetting:-mrow(Typesetting:-mi( 

`/`(5, 4) (6.15)
 

Eller enklare sÃ¥ här med funktionen Typesetting:-mrow(Typesetting:-mi( i maple. 

Typesetting:-mrow(Typesetting:-mi( 

`/`(5, 4) (6.16)
 

Vill man även veta var maximum antas gör man sÃ¥ här. 

Typesetting:-mrow(Typesetting:-mi( 

`/`(5, 4), {[{t = `+`(`*`(`/`(1, 10), `*`(ln(2))))}, `/`(5, 4)]} (6.17)
 

Sedan kan man med lämplig indexering plocka ut det man är intresserad av. 

Typesetting:-mrow(Typesetting:-mi( 

`/`(5, 4) (6.18)
 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`*`(`/`(1, 10), `*`(ln(2)))) (6.19)