Homogeneous Differential Equation with Constant Coefficients Can somebody help me with this problem? I don't know what p
Posted: Sat Jul 09, 2022 1:58 pm
Homogeneous Differential Equation with Constant Coefficients
Can somebody help me with this problem? I don'tknow what part of the script gives me the wrong values etc.Thank you in advance.
Homogeneous Differential Equation with Constant Coefficients MATLAB can solve differential equations using the dsolve command. dsolve Symbolic solution of ordinary differential equations. Example: syms y(x) Dy(x) = diff(y) D2y(x) = diff(y, 2) yGS1 = dsolve (D2y+2*Dy+y==0) yGS2 = dsolve (D2y+2*Dy+y==0, y(0)==-1, y(0)==2) Problems: Solve the following differential equations, using the initial conditions when applicable 1. y₁" + 8y₁ + 16y₁ = 0, y₁ (0) = 1, y₁ (0) = 0 2. Y₂" - 3y₂ + 2y2 = 0, y₂(1) = 1, y₂ (1) = 4 3. y3" + 8y₂ + 17y3 = 0 4. y + 8y + 16y4 = 0 5. y-729y5 = 0
Script 1 %Solve the given Homogeneous Differential Equations with Constant Coefficients 2 %Initialize the Variables 3 clc, clear all 4 syms y(x) 5 Dy(x)=diff(y); 6 D2y(x)=diff(y, 2); 7 D3y(x)=diff(y, 3); 8 D4y(x)=diff(y, 4); 9 D5y(x)=diff(y, 5); 10 D6y(x)=diff(y,6); 11 % Solve the equation y"+8y'+16y=0, y(0)=1, y' (0)=0. Save your answer as y1; 12 y1=dsolve (D2y+8*Dy+16*y==0, y(0)==1, Dy (0)==0) 13 %Solve the equation y"-3y' +2y=0, y_2(1)=1, y_2¹ (1)=4. Save your answer as y2; 14 y2=dsolve (D2y-3*Dy+2*y==0, y(1) ==1, Dy(1)==4) 15 %Solve the equation y"+8y' +17y=0. Save your answer as y3; 16 y3=dsolve (D2y+8*Dy+17*y==0) 17 % Solve the equation y^{IV} + 8y" + 16y=0. Save your answer as y4; 18 y4=dsolve (D4y+8*D2y+16*y==0) 19 %Solve the equation y^{VI}-729y=0. Save your answer as y1; 20 y1=dsolve (D6y-729*y==0) Save C Reset MATLAB Documentation ▶ Run Script
Assessment: 3 of 10 Tests Passed (30%) Y1 * Y2 Y3 * Y4 * Y5 Derivatives Derivative Initialization Function Use Function Use Submit 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 10% (10%) 10% (10%) 10% (10%) Total: 30%
Output y1 = exp(-4*x) * (4*x + 1) y2 = -exp(-2)*exp(x) * (2*exp(1) - 3*exp(x)) y3 = C1*exp(-4*x) *cos(x) - C2*exp(-4*x)*sin(x) y4 = (1*cos(2*x) - C3* sin(2*x) + C2*x*cos(2*x) - (4*x*sin(2*x) y1 = C1*exp(-3*x) + C2*exp(3*x) + C3*exp(-(3*x)/2)*cos((3*3^(1/2) *x)/2) + C5*exp((3*x)/2)*cos((3*3^(1/2)*x)/2) - C4*exp(-(3*x)/2)*sin((3*3^(1/2) 4 © 2020 The MathWorks Inc.
Can somebody help me with this problem? I don'tknow what part of the script gives me the wrong values etc.Thank you in advance.
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Script 1 %Solve the given Homogeneous Differential Equations with Constant Coefficients 2 %Initialize the Variables 3 clc, clear all 4 syms y(x) 5 Dy(x)=diff(y); 6 D2y(x)=diff(y, 2); 7 D3y(x)=diff(y, 3); 8 D4y(x)=diff(y, 4); 9 D5y(x)=diff(y, 5); 10 D6y(x)=diff(y,6); 11 % Solve the equation y"+8y'+16y=0, y(0)=1, y' (0)=0. Save your answer as y1; 12 y1=dsolve (D2y+8*Dy+16*y==0, y(0)==1, Dy (0)==0) 13 %Solve the equation y"-3y' +2y=0, y_2(1)=1, y_2¹ (1)=4. Save your answer as y2; 14 y2=dsolve (D2y-3*Dy+2*y==0, y(1) ==1, Dy(1)==4) 15 %Solve the equation y"+8y' +17y=0. Save your answer as y3; 16 y3=dsolve (D2y+8*Dy+17*y==0) 17 % Solve the equation y^{IV} + 8y" + 16y=0. Save your answer as y4; 18 y4=dsolve (D4y+8*D2y+16*y==0) 19 %Solve the equation y^{VI}-729y=0. Save your answer as y1; 20 y1=dsolve (D6y-729*y==0) Save C Reset MATLAB Documentation ▶ Run Script
Assessment: 3 of 10 Tests Passed (30%) Y1 * Y2 Y3 * Y4 * Y5 Derivatives Derivative Initialization Function Use Function Use Submit 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 0% (10%) 10% (10%) 10% (10%) 10% (10%) Total: 30%
Output y1 = exp(-4*x) * (4*x + 1) y2 = -exp(-2)*exp(x) * (2*exp(1) - 3*exp(x)) y3 = C1*exp(-4*x) *cos(x) - C2*exp(-4*x)*sin(x) y4 = (1*cos(2*x) - C3* sin(2*x) + C2*x*cos(2*x) - (4*x*sin(2*x) y1 = C1*exp(-3*x) + C2*exp(3*x) + C3*exp(-(3*x)/2)*cos((3*3^(1/2) *x)/2) + C5*exp((3*x)/2)*cos((3*3^(1/2)*x)/2) - C4*exp(-(3*x)/2)*sin((3*3^(1/2) 4 © 2020 The MathWorks Inc.