In each of Problems 1-11, solve the initial value problem for the given system. 1. x′−2y′=1,x′+y−x=0;x(0)=y(0)=0 2. 2x′−3y+y′=0,x′+y′=t;x(0)=y(0)=0 3. x′+2y′−y=1,2x′+y=0;x(0)=y(0)=0 4. x′+y′−x=cos(t),x′+2y′=0;x(0)=y(0)=0 5. 3x′−y=2t,x′+y′−y=0;x(0)=y(0)=0 6. x′+4y′−y=0,x′+2y=e−t;x(0)=y(0)=0 7. x′+2x−y′=0,x′+y+x=t2;x(0)=y(0)=0

Solution: To solve the initial value problem for the system of differential equations: 1. x' + 2x - y' = 0

Resuelto In each of Problems 1-11, solve the initial value

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Pregunta: In each of Problems 1-11, solve the initial value problem for the given system. 1. x′−2y′=1,x′+y−x=0;x(0)=y(0)=0 2. 2x′−3y+y′=0,x′+y′=t;x(0)=y(0)=0 3. x′+2y′−y=1,2x′+y=0;x(0)=y(0)=0 4. x′+y′−x=cos(t),x′+2y′=0;x(0)=y(0)=0 5. 3x′−y=2t,x′+y′−y=0;x(0)=y(0)=0 6. x′+4y′−y=0,x′+2y=e−t;x(0)=y(0)=0 7. x′+2x−y′=0,x′+y+x=t2;x(0)=y(0)=0

only 7 is needed

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Hay 2 pasos para resolver este problema.
Solución
Paso 1
Solution:

To solve the initial value problem for the system of differential equations:
1. $x^{'} + 2 x - y^{'} = 0$
Mira la respuesta completa
Paso 2
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Respuesta
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Texto de la transcripción de la imagen:

In each of Problems 1-11, solve the initial value problem for the given system. 1.

x^{'} - 2 y^{'} = 1, x^{'} + y - x = 0; x (0) = y (0) = 0

2 x^{'} - 3 y + y^{'} = 0, x^{'} + y^{'} = t; x (0) = y (0) = 0

x^{'} + 2 y^{'} - y = 1, 2 x^{'} + y = 0; x (0) = y (0) = 0

x^{'} + y^{'} - x = cos (t), x^{'} + 2 y^{'} = 0; x (0) = y (0) = 0

3 x^{'} - y = 2 t, x^{'} + y^{'} - y = 0; x (0) = y (0) = 0

x^{'} + 4 y^{'} - y = 0, x^{'} + 2 y = e^{- t}; x (0) = y (0) = 0

x^{'} + 2 x - y^{'} = 0, x^{'} + y + x = t^{2}; x (0) = y (0) = 0