Will someone help me with 11 12 for differential equationsS

Solution

>> Solution 1

Second- Order Differential Equation is :

2*(d²x/dt²) +4*(dx/dt) - 5x = t*e^-3t

>> Let, y = dx/dt

so, dy/dt = d²x/dt²

So, this equation becomes :

=> 2*(dy/dt) + 4*y - 5x = t*e^-3t

and, y = dx/dt .......ANSWER....

>> Solution 2.

Now, two differential equations are :

dx/dt = y,

and , dy/dt = 3x - y + 4*e^t

Putting y = dx/dt in 2nd equation, we get

=> d(dx/dt)/dt = 3x - (dx/dt) + 4*e^t

So, Equation becomes :

(d²x/dt²) + (dx/dt) - 3x = 4*e^t .......ANSWER.....