1.Let y=y(x)y = y(x)y=y(x) be the solution of the DE dydx=(y+1)((y+1)ex2/2−x)\frac{dy}{dx} = (y+1)\left((y+1)e^{x^2/2} - x\right)dxdy=(y+1)((y+1)ex2/2−x), 0<x<2.10<x<2.10<x<2.1, with y(2)=0y(2)=0y(2)=0. Then the value of dydx\frac{dy}{dx}dxdy at x=1x=1x=1 is equal toa.−e3/2(e2+1)2\frac{-e^{3/2}}{(e^2+1)^2}(e2+1)2−e3/2b.−2e2(1+e2)2-\frac{2e^2}{(1+e^2)^2}−(1+e2)22e2c.e5/2(1+e2)2\frac{e^{5/2}}{(1+e^2)^2}(1+e2)2e5/2d.5e1/2(e2+1)2\frac{5e^{1/2}}{(e^2+1)^2}(e2+1)25e1/2Login to continueOnly logged in users canattempt or see the solution.
