11. The respective expressions for complimentary function and particular integral part of the solution of the differential equation $$\frac{{{{\text{d}}^4}{\text{y}}}}{{{\text{d}}{{\text{x}}^4}}} + 3\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 108{{\text{x}}^2}$$ are
12. The solution of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{t}}^2}}} + 2\frac{{{\text{dy}}}}{{{\text{dt}}}} + {\text{y}} = 0$$ with y(0) = y'(0) = 1 is
13. Consider the differential equation $$\left( {{{\text{t}}^2} - 81} \right)\frac{{{\text{dy}}}}{{{\text{dt}}}} + 5{\text{ty}} = \sin \left( {\text{t}} \right)$$ with y(1) = 2π. There
exists a unique solution for this differential equation when t belongs to the interval
14. The solution to 6yy' - 25x = 0 represents a
15. Which one of the following is the general solution of the first order differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = {\left( {{\text{x}} + {\text{y}} - 1} \right)^2},$$ where x, y are real?
16. If roots of the auxiliary equation of $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + {\text{a}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{by}} = 0$$ are real and equal, the general solution of the differential equation is
17. The solution of the ordinary differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{2y}} = 0$$ for the boundary condition, y = 5 at x = 1 is
18. If y is the solution of the differential equation
$$\eqalign{
& {{\text{y}}^3}\frac{{{\text{dy}}}}{{{\text{dx}}}} + {{\text{x}}^3} = 0, \cr
& {\text{y}}\left( 0 \right) = 1 \cr} $$
the value of y(-1) is
$$\eqalign{ & {{\text{y}}^3}\frac{{{\text{dy}}}}{{{\text{dx}}}} + {{\text{x}}^3} = 0, \cr & {\text{y}}\left( 0 \right) = 1 \cr} $$
the value of y(-1) is