Question

Solve the given integral equation or integro-differential equation for y(t). y'CL)+ 125 ſ <t-vy(v) dv=7! y(0)=0 0 y(t) = Enter your answer in the answer box.

Answer 1

ot y(O) = 0 = 7 Now. The given Integmo- differential equation is? Y'() + 125. ( (t-v).960).dv = 7t taking Laplace transform both sides we get → L{y'lt)} + 125.4 S ce-v) Xudv 7.L{t} 5 LÝs(t)} - (6) + 125 L{t). L{3(} = 1 (5 + 125 ): 4490)} 183 +125) L{y(ty= = S² > Is 1 Hold 7 DEL s² s²

7 7 L{y()} = (s}+125) - A) ㅋ .L{y(t)} (5+5) (82-55+25) 7 (༩༠) - རོ ་ , ཙེ , * (s+5). [ 7 (s+5).[15-]{+(5*] Nowo, taking Laplace In Verse transform both Sides We get = 30= 7c'{ [sts)[{4+ =CE Now, L ..Now, +++(91 (s +5): [[3- $+ (**) (29} -est. = f(0) 활 ?+(58)] 2 + ( ( $24). = 964) } s +5 e L Lola 2 573 sin

::New LYS (s+s)[(5= )2+(**)_] potreberste) }(t-x). g(x).dx. O -5(1-x) 2 ex sin (572x) dx 513 0 -st 2 513 24.com (m). .da E Re-st 513 513 * sin(stan) - Sapa Cos ( ( 4592 +1 58503 h ( 5 ) s(53) 0 Rest 15 2 sin 513 2 Los 513 75 1513 + х 2 75 - -5t e e + 75 - [18:51-60] Therefore, YCB) This is required Solution 7 75 V3 Sin (5X2)- -st Cos cent