Question

Solve the given integral equation or integro-differential equation for y(t). V'(t)+125] (t-v)/(v) dv=5t, y) = 0 125 ſe-vrye y()=

Answer 1

0 The above st Y'14) + 125 Sct.wylvdv = 57 y (0)=0 eq can be written 4 (6) (+) - 1257 Taking tap lace Trans form both sides, we get Lly') & 125 hlt) Llylt)) = 5L(t) = SY(s)- syco) - 125 Yls) ( (4) = 5 S2 $2 YO3) [s* 125 -] S2 82 ie Y(8) 5 [ 395,125) sa - Y(S) 5 S3125 5 је (5-5) (8² +55+25) using partial fraction decomposition, S-5 BSTC + (5-5) (8² +55+25) 8458425 => 1 = A(+58 +a5) + (B.S+) (8-5) = 1 = CA+B) 8² + (5A+C-5B8 +25A-SC get A+B=0 = A=-B 5AT C-SB=0 SA+c+5A=0 -) 10 Atc=0 & - C=-10A 25A- 5C = 1 on companing we Also,