Find the solution of the given initial value problem in explicit form. y' = (1 – 11x)y?, y(0) = -1 Enclose numerators and denominators in parentheses. For example, (a - b)/(1 + n). y(x) = Q

Answer:[tex]y(x)=-e^{x-(\frac{11*x^{2} }{2}) }[/tex]Step-by-step explanation:This is a separable equation. First divide both sides by y:[tex]\frac{dy(x)}{\frac{dx}{y(x)} } =-11x+1\\\frac{dy}{y}=(-11x+1)dx[/tex]Integrate both sides:[tex]\int\ \frac{dy}{y} \ =\int\ (-11x+1) \, dx[/tex][tex]log(y)=-(\frac{11*x}{2} )+x+ c_1[/tex]Solve for y taking exp to both sides:[tex]y(x)=c_1*e^{x-(\frac{11*x^{2} }{2}) }[/tex]Where [tex]c_1[/tex] is an arbitrary constantEvaluating the initial condition:[tex]y(0)=c_1*e^{0-(\frac{11*0^{2} }{2}) } =-1[/tex][tex]c_1*e^{0} =-1\\c_1*1=-1\\c_1=-1[/tex]Finally, replacing [tex]c_1[/tex] in the differential equation solution:[tex]y(x)=-e^{x-(\frac{11*x^{2} }{2}) }[/tex]