Ordinary differential equations questions.

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#	Question
1	Define the terms order and degree of a differential equation. State the order and degree of the following differential equation $3(y{}')^{3}+4(y`)^{10}+3y^{4}=0$ Mathematical Calculation
2	Solve the following differential equation $(ycosx+2xe^{y})+(sinx+x^{2}e^{y}-1)y`=0$ Mathematical Calculation
3	Show that $y_{1}(t)=t^{frac{1}{2}}$ and $y_{2}(t)=t^{-1}$ form a fundamental set of solutions of $2t^{2}y{}'+3ty{}`-y=0, t>0$ Mathematical Calculation
4	Solve $y{}'-3y`-18y=xe^{4x}$ Mathematical Calculation
5	Use the method of variation of parameters to solve the differential equation $y{}'+y=sec,x, 0<x<frac{pi}{2}$ Mathematical Calculation
6	Solve the IVP $y{}`=frac{xy^{3}}{sqrt{1+x^{2}}}, y(0)=-1$ and find the interval of validity of the solution. Mathematical Calculation
7	Show that by using polar transformation the differential equation $(x+y)dx-(x-y)dy=0$ can be reduced to a variable separable differential equation $frac{dr}{d heta}=r$ Mathematical Calculation
8	Solve the differential equation $xy`-2y=4x^{3}y^{frac{1}{2}}$ Mathematical Calculation
9	If f, g and h are differentiable functions, show that $W(fg,fh)=f^{2}W(g,h)$ Mathematical Calculation
10	Show that if p is differentiable and p(t)>0 the Wronskian W(t) of two solutions of $[p(t)y`]`+q(t)y=0$ is $W(t)=frac{c}{p(t)}$ where c is constant. Mathematical Calculation