Determine whether you have the following differential equations: order, or non-order, linear or non-linear, constant or...

 

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Determine whether you have the following differential equations: order, or non-order, linear or non-linear, constant or variable. (8%) (1) y +2y = sinx+1 (2) y"+y'sin2x+xy=0 (3) xy" + 3xy - xy = sin 3x (4) y"+ex-y=0 It was observed that the rate of change in the population of bacteria was proportional to the total population. Find a differential equation in which N(t) represents the number of objects in time t, and when using the proportional constant k the change in the number of objects over time, and find a general solution. (5%) Throw a stone of mass m from the ground to the air with a force of F1, the initial velocity at time 0 is called V1. Using Newton's second law of motion, establish a differential equation that expresses the relative height z of a stone relative to the ground as a function of time and obtain a general solution. (7%) Find the solution of the following first-order differential equation. (9%)) (1) y'-y = 5.2 (2) y + ky=e-kr (3) y + 2y = 4 cos 2x, y()=3 Proliferation of cancer cells (7%) The size (volume) V of a cancer cell is expressed by the following equation over time for any two positive constants a and X. dV dt = Aeat V Find an expression for the initial condition v(0) = Vo, the size of the cancer cell. Determine whether you have the following differential equations: order, or non-order, linear or non-linear, constant or variable. (8%) (1) y +2y = sinx+1 (2) y"+y'sin2x+xy=0 (3) xy" + 3xy - xy = sin 3x (4) y"+ex-y=0 It was observed that the rate of change in the population of bacteria was proportional to the total population. Find a differential equation in which N(t) represents the number of objects in time t, and when using the proportional constant k the change in the number of objects over time, and find a general solution. (5%) Throw a stone of mass m from the ground to the air with a force of F1, the initial velocity at time 0 is called V1. Using Newton's second law of motion, establish a differential equation that expresses the relative height z of a stone relative to the ground as a function of time and obtain a general solution. (7%) Find the solution of the following first-order differential equation. (9%)) (1) y'-y = 5.2 (2) y + ky=e-kr (3) y + 2y = 4 cos 2x, y()=3 Proliferation of cancer cells (7%) The size (volume) V of a cancer cell is expressed by the following equation over time for any two positive constants a and X. dV dt = Aeat V Find an expression for the initial condition v(0) = Vo, the size of the cancer cell.