Determine whether the following statements are True or False. A point will be given for every right answer, and half of a point will be deducted for every wrong answer. If there is no answer, no points will be given or deducted. An unclear answer counts as a wrong answer. A bonus point will be given if there are no wrong answers.The solution of the initial value problemdydx=y2-2y,y(1)=1is an increasing function.2. If y(x) is the solution of the initial value problemdydx=y2-2y,y(1)=1thenlimxy(x)=0.For every solution y(x) of the linear equationy'xy=xit is true thatlimxy(x)=1The solution of the initial value problemdydx=2xy2,y(0)=1is defined on the whole real line.5. The largest interval on which the solution of the initial value problem (as above)dydx=2xy2,y(0)=1is defined is (-1,1).6. Let A be the largest number such that the solution ofdydx=(y1)2,y(0)=0is defined on the half-line (-,A). Then A=1.7. If y(x) is the solution of the initial value problemxdydx2y=1,y(1)=0,thenlimxy(x)=1There exists a function F of two variables x,y such thatdF=(x-y)dx(xy)dyThe constant solution y=0 of the equationy'=sinyis stable.10. If y(x) is the solution of the initial value problemy'=siny,y(0)=1,thenlimxy(x)=