Ordinary differential equations questions.

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#	Question
1	Given that $y_{1}(t)=t^{-1}$ is a solution of $2t^{2}y{}' +3y`-y=0,,,,t>0$ find a second linearly independent solution. Mathematical Calculation
2	Solve the differential equation $y{}'-3y`-4y=2,sin,x$ Mathematical Calculation
3	Determine if the power series method yields a solution around x=0 to the differential equation $y{}'-2xy`-2y=0$ Is x=0 an ordinary or singular point of the equation ? If x=0 is ordinary, find the power series solution of the equation around it. Mathematical Calculation
4	Solve the Cauchy-Euler differential equation $x^{2}y{}'+xy`-y=0$ using Frobenius method. Mathematical Calculation
5	Given the equation $x(x-1)y{}'+(3x-1)y`+y=0$ . Determine the singular points of the equation. Mathematical Calculation
6	Transform the second order differential equation into systems of first order differential equations $x`+8x+y'=12$ Mathematical Calculation
7	Reduce the system of first order differential equations into a second order differential equation $x`=x+2y,,,,y`=2x-y$ By using the elimination method, solve the system of first order differential equations in (a) above. Mathematical Calculation
8	Solve the initial value problem $y`=10-0.2y,,,,y(0)=50$ Mathematical Calculation
9	Classify the following differential equation as to order, degree and linearity $y```=y`+(y')^{2}$ Mathematical Calculation
10	Find the solution of the IVP $(12-4x^{2}y)y`=4xy^{2}+8,,,y(-1)=8$ Mathematical Calculation