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d1= 3 and d2= 2 Question 1 ch- 3, d2 - 2 (a) Find the most general solution u(x, y) of the two PDEs Lt +1) y cos y +(di +1)x cos ((d, +1)xy)+2x d2 (b) Find the solution that satisfies initial condit...
d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram bel...
d1= 3 & d2= 2
Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
d1=8 d2=9 lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero in...
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solutio...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0
1. Consider the Partial Differential Equation ot u(0,t) =...
and determine in which regions the given PDE’s are elliptic/ hyperbolic/ parabolic Problem 3 Find all solution of the following PDEs 1. 2. --= y, u=u(z, y). Problem 3 Find all solution of th...
and determine in which regions the given PDE’s are elliptic/
hyperbolic/ parabolic
Problem 3 Find all solution of the following PDEs 1. 2. --= y, u=u(z, y).
Problem 3 Find all solution of the following PDEs 1. 2. --= y, u=u(z, y).
Find a solution 3. (1+x)y' + y = cos 2x.
Find a solution
3. (1+x)y' + y = cos 2x.
find a solution 3. (1 + x)y' + y = cos 2x.
find a solution
3. (1 + x)y' + y = cos 2x.
using the general power rule Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2...
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution...
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"-...
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"- 2y'- 15y=-51 sin(3 x) -3x | Ae 5x + Be 34 y(x) = 8.5 + -cos(3x) * 17 51 14 sin(3x) - - Find the unique solution that satisfies the initial conditions: Y(0) = 2.5 and y'(o)=37 y(x) = 7. [-12 Points) DETAILS Find the general (real) solution of the differential equation: y" + 4y' + 4y=64 cos(2x) y(x) = Find the unique solution...
D1 = 7 D2 = 4 Any assistance would be greatly appreciated Question 3 Left end (x 0) of a copper rod of length 100mm is kept at a constant temperature of Temp - 10+d2 degrees and the right end and...
D1 = 7
D2 = 4
Any assistance would be greatly appreciated
Question 3 Left end (x 0) of a copper rod of length 100mm is kept at a constant temperature of Temp - 10+d2 degrees and the right end and sides are insulated, so that the temperature in the rod, u(x,t). obeys the heat partial DE, CD11 mms copper. where D-1 mm's for copper (a) Write the boundary conditions for u(x, 1) of the problem above. Note that for...
d1= 3 & d2= 2
Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0
1. Consider the Partial Differential Equation ot u(0,t) =...
and determine in which regions the given PDE’s are elliptic/
hyperbolic/ parabolic
Problem 3 Find all solution of the following PDEs 1. 2. --= y, u=u(z, y).
Problem 3 Find all solution of the following PDEs 1. 2. --= y, u=u(z, y).
Find a solution
3. (1+x)y' + y = cos 2x.
find a solution
3. (1 + x)y' + y = cos 2x.
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"- 2y'- 15y=-51 sin(3 x) -3x | Ae 5x + Be 34 y(x) = 8.5 + -cos(3x) * 17 51 14 sin(3x) - - Find the unique solution that satisfies the initial conditions: Y(0) = 2.5 and y'(o)=37 y(x) = 7. [-12 Points) DETAILS Find the general (real) solution of the differential equation: y" + 4y' + 4y=64 cos(2x) y(x) = Find the unique solution...
D1 = 7
D2 = 4
Any assistance would be greatly appreciated
Question 3 Left end (x 0) of a copper rod of length 100mm is kept at a constant temperature of Temp - 10+d2 degrees and the right end and sides are insulated, so that the temperature in the rod, u(x,t). obeys the heat partial DE, CD11 mms copper. where D-1 mm's for copper (a) Write the boundary conditions for u(x, 1) of the problem above. Note that for...
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