Why we get this ans R5.6.7.8.ale ale sale||dx y + eyx²1+ y²dx|| || ||| آبادyIn each of Problems 9 through 16:a. Find the solution of the given initial value problem in explicitform.G b. Plot the graph of the solution.c. Determine (at least approximately) the interval in which thesolution is defined.y' = (1-2x) y²,y'=(1-2x)/y,9.y(0) = -1/610.y(1) = −211.xdx+ye dy = 0, y(0) = 112.dr/d0 = r²/0, r(1) = 213. y'=xy³ (1+x²)-¹/2, y(0) = 114.y'= 2x/(1+2y), y(2) = 0BR15. y'= (3x2 - e*)/(2y-5), y(0) = 116. sin(2x) dx + cos(3y) dy = 0, y(π/2) = π/3Some of the results requested in Problems 17 through 22 can beobtained either by solving the given equations analytically or byplotting numerically generated approximations to the solutions. Tryto form an opinion about the advantages and disadvantages of eachapproach.G 17. Solve the initial value problemy':=1+3x²3y² - 6yy(0) = 1and determine the interval in which the solution is valid.Hint: To find the interval of definition, look for points where theintegral curve has a vertical tangent.G 18. Solve the initial value problem3x²and c23.wher24.wherbehaHomdy/onlycanthe dhom R5.6.7.8.ale ale sale||dx y + eyx²1+ y²dx|| || ||| آبادyIn each of Problems 9 through 16:a. Find the solution of the given initial value problem in explicitform.G b. Plot the graph of the solution.c. Determine (at least approximately) the interval in which thesolution is defined.y' = (1-2x) y²,y'=(1-2x)/y,9.y(0) = -1/610.y(1) = −211.xdx+ye dy = 0, y(0) = 112.dr/d0 = r²/0, r(1) = 213. y'=xy³ (1+x²)-¹/2, y(0) = 114.y'= 2x/(1+2y), y(2) = 0BR15. y'= (3x2 - e*)/(2y-5), y(0) = 116. sin(2x) dx + cos(3y) dy = 0, y(π/2) = π/3Some of the results requested in Problems 17 through 22 can beobtained either by solving the given equations analytically or byplotting numerically generated approximations to the solutions. Tryto form an opinion about the advantages and disadvantages of eachapproach.G 17. Solve the initial value problemy':=1+3x²3y² - 6yy(0) = 1and determine the interval in which the solution is valid.Hint: To find the interval of definition, look for points where theintegral curve has a vertical tangent.G 18. Solve the initial value problem3x²and c23.wher24.wherbehaHomdy/onlycanthe dhom

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6. 7 dy dx dy = x² 1 + y² y