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Solve the following equation by Laplace transforms dx +3x=e dt given that x= 2 when t=0

Solve the following equation by Laplace transforms dx +3x=e dt given that x= 2 when t=0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a (x, v) a(x.t) For 0Sxsl with a step length h=0.2 and 0SIS0.2 with a step length k =0.02 where (x.0) = x (0,t)=0 and of (x, y) = 0.25 6. Use the Newton-Raphson iterative method to solve the following: Show that a root of the equation x+3x +5x+9=0 occurs between x = -2 and x -3. Evaluate the roots to 4 significant figures Show that the equation x+3sin x=2 has a root between x = 0.8 and x = 0.6. ii. Evaluate the root correct to 5 significant figures. ii. Given the table of values f(x) -2.63906 -2 -2.48491 -1.94591 -1.79176 Use Langrangian interpolation find the Value of (a) fl-0.8) (b) f(0.8) (c) f(5.5)
Transcribed Image Text:a (x, v) a(x.t) For 0Sxsl with a step length h=0.2 and 0SIS0.2 with a step length k =0.02 where (x.0) = x (0,t)=0 and of (x, y) = 0.25 6. Use the Newton-Raphson iterative method to solve the following: Show that a root of the equation x+3x +5x+9=0 occurs between x = -2 and x -3. Evaluate the roots to 4 significant figures Show that the equation x+3sin x=2 has a root between x = 0.8 and x = 0.6. ii. Evaluate the root correct to 5 significant figures. ii. Given the table of values f(x) -2.63906 -2 -2.48491 -1.94591 -1.79176 Use Langrangian interpolation find the Value of (a) fl-0.8) (b) f(0.8) (c) f(5.5)
Tutorial Ques 1. Solve the following equation by Laplace transforms dr (a) +3x =e given that x = 2 when t = 0 dt (b) 3x-6x = sin 2t given that x=1 when t=0 (c) x-7x+12x = 2 given that at t= 0, x =1 and x =5 (d) x-2x+x = te given that at t = 0, x = 1 and x=0 2. Use the Newton-Raphson iterative method to solve the following: Show that a root of the equation x +3x + 5x+9 =0 occurs between x = -2 and x = -3. Evaluate the roots to 4 significant figures i. i. Show that the equation x+3sinx=2 has a root between x = 0.8 and x = 0.6. Evaluate the root correct to 5 significant figures. The equation 20x -22x + 5x -1=0 has a root at approximately x = 0.6. Determine the value of the root correct to 4 significant figures. iii. 3. Solve the equation numerically 5. .4 =-5 For 0Sxs1 with a step length h = % and 0s ysi with a step length k = %/- where f(x,0) = 3x-4 f(x,1) = 3x+1 f(0,y)=5y-4 f(1,y)=5y-1 4. Solve the following equations 2-5x+1=0 i. ii. x'+2x-3=0 i. -4x+1=0 5. Solve the equation numerically using the forward difference approximation for the first derivative with respect to time
Transcribed Image Text:Tutorial Ques 1. Solve the following equation by Laplace transforms dr (a) +3x =e given that x = 2 when t = 0 dt (b) 3x-6x = sin 2t given that x=1 when t=0 (c) x-7x+12x = 2 given that at t= 0, x =1 and x =5 (d) x-2x+x = te given that at t = 0, x = 1 and x=0 2. Use the Newton-Raphson iterative method to solve the following: Show that a root of the equation x +3x + 5x+9 =0 occurs between x = -2 and x = -3. Evaluate the roots to 4 significant figures i. i. Show that the equation x+3sinx=2 has a root between x = 0.8 and x = 0.6. Evaluate the root correct to 5 significant figures. The equation 20x -22x + 5x -1=0 has a root at approximately x = 0.6. Determine the value of the root correct to 4 significant figures. iii. 3. Solve the equation numerically 5. .4 =-5 For 0Sxs1 with a step length h = % and 0s ysi with a step length k = %/- where f(x,0) = 3x-4 f(x,1) = 3x+1 f(0,y)=5y-4 f(1,y)=5y-1 4. Solve the following equations 2-5x+1=0 i. ii. x'+2x-3=0 i. -4x+1=0 5. Solve the equation numerically using the forward difference approximation for the first derivative with respect to time
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