at all.SECTION T.2 EXERCISESasIn Probiems 1-10 determine a region of the xy-plane for which the givendifferential equation would have a unique solution through a point (X,, Yo}in the region.h ax2.Vxydyydxdy%3Ddx iven differential equation. In some cases assume an appropriate intervalal equation xy(9) – xy" + 4xy'-3y = 0nt we haven functional with sysx? dy + (y-xy - xe) dx = 0d'y+ 9y == sin y6.more unknoand y dendyfollowing1dr?d'ydxd'r8.= -dxdr?(sin x)y" - (cos x)y'Problems 11-40 verify that the indicated function is a solution of the= 210. (1- y?) dx + x dy = 0validity for the solution. Where used, the symbols c, and c, denote con-ants.1. 2y' +y = 0; y e-212. y' + 4y = 32; y = 8ple functiddytem on soi2y e: y = er + 10e?*dxdy14.+ 20y = 24; y = - e-01dty' = 25 + y; y = 5 tan 5xdy: y= (Vx + c), x > 0, c > 0V xdxations areo need to . y' + y = sin x; y = sin x- cos x + 10e *erms of*. B. 2xy dx + (x + 2y) dy = 0; x'y + y =er y in termnd20 (y') + xy' = y; y = x+ 11e differentio. x dy + 2xy dx = 0; y =example. Afferentiab1. y = 2xy' + y(y')': y? = c(x + c;)ve may r2. y' = 2Viyl: y = xxalgebra.icit solutid3. y'y = 1; y=x In x, x>0- -quation fof symb4.aC;e1+ bcet2- XdPP(a -- bP); P =dtdX5.dt3(2-X)(1-X); in1 -n is linc, y' + 2xy = 1; y=eedt + ce+GeOn is lined,= 0: C(x +y) = re7. (x+ y) dx + (x - xy) dyy = 0 8. y" + y'- 12y = 0; y Ce+ Ce9. y" - 6y' + 13y = 0; y = e cos 2x

Name: at all.SECTION T.2 EXERCISESasIn Probiems 1-10 determine a region of
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Description: at all.SECTION T.2 EXERCISESasIn Probiems 1-10 determine a region of the xy-plane for which the givendifferential equation would have a unique solution through a point (X,, Yo}in the region.h ax2.Vxydyydxdy%3Ddx iven differential equation. In some c