The Blasius equation, $$\frac{{{{\text{d}}^3}{\text{f}}}}{{{\text{d}}{{\text{n}}^3}}} + \frac{{\text{f}}}{2}\frac{{{{\text{d}}^2}{\text{f}}}}{{{\text{d}}{{\text{n}}^2}}} = 0,$$ is a
If the characteristic equation of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 2\alpha \frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{y}} = 0$$ has two equal roots, then the values of $$\alpha $$ are
The solution of the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + \frac{{\text{y}}}{{\text{x}}} = {\text{x}},$$ with the condition that y = 1 at x = 1, is
Consider the following differential equation: $$\frac{{{\text{dy}}}}{{{\text{dt}}}} = - 5{\text{y;}}$$ initial condition: y = 2 at t = 0. The value of y at t = 3 is
Which of the following is a solution to the differential equation $$\frac{{{\text{dx}}\left( {\text{t}} \right)}}{{{\text{dt}}}} + 3{\text{x}}\left( {\text{t}} \right) = 0?$$
The homogenous part of differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + {\text{P}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{qy}} = {\text{r}}$$ (P, q, r are constants) has real distinct roots if
For $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 4\frac{{{\text{dy}}}}{{{\text{dx}}}} + 3{\text{y}} = 3{{\text{e}}^{2{\text{x}}}},$$ the particular integral is
The solution of $${\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{y}} = {{\text{x}}^4}$$ with the condition $${\text{y}}\left( 1 \right) = \frac{6}{5}$$ is
The solution of differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + \frac{{{\text{6dy}}}}{{{\text{dx}}}} + 9{\text{y}} = 9{\text{x}} + 6$$ with C1 and C2 as constant is
