ordinary differential equation

The "order" of the following ordinary differential equation is $\qquad$ . $$ \frac{d^3 y}{d x^3}+\left(\frac{d^2 y}{d x^2}\right)^6+\left(\frac{d y}{d x}\right)^4+y=0 $$

The differential equation, $\rm \frac{du}{dt}+2tu^2=1,$ is solved by employing a backward difference scheme within the finite difference framework. The value of 𝑢 at the (𝑛 − 1)...

For the equation $${{{d^3}y} \over {d{x^3}}} + x{\left( {{{dy} \over {dx}}} \right)^{3/2}} + {x^2}y = 0$$ the correct description is

The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is

The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is

The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \over {d\,x}}} \right)_{x = {\raise0.5ex\hbox{$\scriptstyle \pi...

Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ i...

The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$

Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$ $$y\left( 0 \right) = 3$$ and $${y^1}\left( 0 \right) = 1,$$ where prime denotes derivative...

Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$