Uppgift 3.5(Appl): 1, 3, 6. Variation av parametrar. 

Typesetting:-mrow(Typesetting:-mi( 

Uppgift 6 

Övriga uppgifter löses helt analogt. Se ocksÃ¥ exempel 11 pÃ¥ sidan 208 i läroboken. 

Typesetting:-mrow(Typesetting:-mi( 

`+`(diff(diff(y(x), x), x), `-`(`*`(2, `*`(diff(y(x), x)))), `*`(2, `*`(y(x)))) = h (5.1)
 

Typesetting:-mrow(Typesetting:-mi( 

y(x) = `+`(`*`(_C1, `*`(exp(x), `*`(sin(x)))), `*`(_C2, `*`(exp(x), `*`(cos(x))))) (5.2)
 

Typesetting:-mrow(Typesetting:-mi( 

`*`(exp(x), `*`(cos(x))) (5.3)
 

Typesetting:-mrow(Typesetting:-mi( 

`*`(exp(x), `*`(sin(x))) (5.4)
 

Wronskideterminanten 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`*`(exp(x), `*`(cos(x), `*`(`+`(`*`(exp(x), `*`(sin(x))), `*`(exp(x), `*`(cos(x))))))), `-`(`*`(exp(x), `*`(sin(x), `*`(`+`(`*`(exp(x), `*`(cos(x))), `-`(`*`(exp(x), `*`(sin(x)))))))))) (5.5)
 

förenklas till 

Typesetting:-mrow(Typesetting:-mi( 

exp(`+`(`*`(2, `*`(x)))) (5.6)
 

Högerledet. 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`*`(12, `*`(`^`(x, 2), `*`(exp(x), `*`(sin(x)))))) (5.7)
 

Partikulärlösningen 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`-`(`*`(exp(x), `*`(cos(x), `*`(`+`(`*`(12, `*`(`^`(x, 2), `*`(`+`(`-`(`*`(`/`(1, 2), `*`(cos(x), `*`(sin(x))))), `*`(`/`(1, 2), `*`(x)))))), `-`(`*`(6, `*`(x, `*`(`^`(cos(x), 2))))), `*`(3, `*`(c...
`+`(`-`(`*`(exp(x), `*`(cos(x), `*`(`+`(`*`(12, `*`(`^`(x, 2), `*`(`+`(`-`(`*`(`/`(1, 2), `*`(cos(x), `*`(sin(x))))), `*`(`/`(1, 2), `*`(x)))))), `-`(`*`(6, `*`(x, `*`(`^`(cos(x), 2))))), `*`(3, `*`(c...		 (5.8)
 

kan snyggas till först sÃ¥ här 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`-`(`*`(exp(x), `*`(`+`(`-`(`*`(3, `*`(sin(x), `*`(`^`(x, 2))))), `*`(3, `*`(sin(x))), `*`(2, `*`(cos(x), `*`(`^`(x, 3)))), `-`(`*`(3, `*`(x, `*`(cos(x)))))))))) (5.9)
 

och sedan sÃ¥ här 

Typesetting:-mrow(Typesetting:-mi( 

`+`(`-`(`*`(`+`(`-`(`*`(3, `*`(`^`(x, 2)))), 3), `*`(exp(x), `*`(sin(x))))), `-`(`*`(`+`(`-`(`*`(3, `*`(x))), `*`(2, `*`(`^`(x, 3)))), `*`(exp(x), `*`(cos(x)))))) (5.10)
 

Typesetting:-mrow(Typesetting:-mi( 

Plot_2d