Question

Solve the following homogeneous system of first order ODE: \frac{dx}{dt} = 6x - 4y; \frac{dy}{dt} = 4x - 2y with initial conditions: x(0) = 1, y(0) = 2.

          Solve the following homogeneous system of first order ODE:
\frac{dx}{dt} = 6x - 4y;
\frac{dy}{dt} = 4x - 2y
with initial conditions: x(0) = 1, y(0) = 2.
        
Solve the following homogeneous system of first order ODE:
(dx)/(dt) = 6x - 4y;
(dy)/(dt) = 4x - 2y
with initial conditions: x(0) = 1, y(0) = 2.

Added by Shannon M.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Solve the following homogeneous system of first-order ODE: dx/dt = 6x - 4y dy/dt = 4x - 2y with initial conditions: x(0) = 1, y(0) = 2.
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Transcript

-
00:01 Friends, in this question we are given with three differential equations.
00:03 So, we have to find the solution according to this.
00:06 So, first one is the homogeneous equation.
00:08 So, we take d squared minus 2d plus 10 into y which equal to zero.
00:12 So, the auxiliary equation become d squared minus 2d plus 10 equal to zero.
00:17 Therefore, roots are 1 plus or minus 3i.
00:20 So, the solution y equal to e power x into c1 cos 3x plus c2 sin 3x.
00:26 The second one is homogeneous equation.
00:28 So, we take 3d squared minus 2d plus 1 into y equal to zero.
00:33 So, the auxiliary equation is 3d squared minus 2d plus 1 equal to zero.
00:37 So, the roots are 1 by 3 plus or minus root 2 divided by 3.
00:42 So, y equal to c, y equal to e power 1 by 3x into c1 cos root 2 divided by 3x plus c2 sin root 2 divided by 3 into x...
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