00:01
In this question, we are given four differential equations and four different graphs.
00:06
And we have to match the graph of the solutions with the given, we have to match the solutions of each of this differential equation with the given graphs.
00:17
So let's find the equation, find the solutions first of the given differential equation.
00:23
So first differential equation is x double dash plus 4x is equal to 0.
00:32
So it can be, you know, if i let d is equal to, if i let d is equal to d divided by d, y, so it will become d square x plus 4x equals to 0.
00:53
Now taking x common, i will get d square plus 4 multiplied to x is equal to 0.
01:01
Now x cannot be equals to 0 and that's why i will say that d square plus 4 equals to 0.
01:08
0 right now on solving this and trying to get the value of d i will get two imaginary numbers that is plus minus two iota and hence the solution of this differential equation will be x is equals to x is equals to c1 where c1 c2 are constants so c1 cos 2 y plus c2 sine 2 y so this is a solution of the first differential equation.
01:56
The second differential equation is almost similar.
01:59
So the second differential equation is x double dash minus 4 x is equals to 0.
02:07
Solving it similarly like we did in the first equation.
02:12
So it will be d square minus 4 x equals to 0.
02:18
And so we get two values of d which are real and that are 2 and minus 2.
02:22
And hence, in this case, the solution of differential equation will be x is equals to c1 e raised to the power 2y plus c2e raise to the power minus 2y.
02:39
So this is a solution of the second differential equation...