Homogeneous Differential Equations
26:55
YouTubeThe Organic Chemistry Tutor
Homogeneous Differential Equations
This calculus video tutorial provides a basic introduction into solving first order homogeneous differential equations by putting it in the form M(x,y)dx + N(x,y)dy = 0. You can solve it by substitution using the equation y = vx and dy = xdv + vdx. Following the change of variables, you can integrate the differential equation by separation of ...
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3.(a) Give an example of a differential equation that has exactly one solution.(Note: Your differential equation must contain y(x) and its derivative[2 marks]y'(x).)(b) Show that the following four functions are linearly independent:1, e^-2x, cos(3x), and sin(3x).[5 marks](c) Find a homogeneous linear differential equation that has these functions as solutions,i.e., find a homogeneous linear differential equation with general solutionyc(x) = c1 c2 e^-2x c3 cos(3x) c4 sin(3x).[4 marks]
3.(a) Give an example of a differential equation that has exactly one solution.(Note: Your differential equation must contain y(x) and its derivative[2 marks]y'(x).)(b) Show that the following four functions are linearly independent:1, e^-2x, cos(3x), and sin(3x).[5 marks](c) Find a homogeneous linear differential equation that has these functions as solutions,i.e., find a homogeneous linear differential equation with general solutionyc(x) = c1 c2 e^-2x c3 cos(3x) c4 sin(3x).[4 marks]
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