1. Show that y1=cosx and y2=sinx are solution of the DE y''+y=0.verify that ⱷ(x)=c1cosx+c2sinx is also a solution of the DE.
2. Given that y1 and y2 are the solution of the DE y''+y^2=0. Is y3 =c1y1+c2y2 also a solution of the DE?
1. Show that y1=cosx and y2=sinx are solution of the DE y''+y=0.verify that ⱷ(x)=c1cosx+c2sinx is also a solution of the DE.
2. Given that y1 and y2 are the solution of the DE y''+y^2=0. Is y3 =c1y1+c2y2 also a solution of the DE?
Just to let the helpers here know, this question has also been posted at MMF, and I have offered hints on how to proceed.
For the first one, you will need to find and substitute into the given ODE.
For the second one, you are told:
Multiply the first equation by and the second by , then add the equations. What do you find?