initial value problem

Consider differential equation $\frac{dy}{dx} + xy = x$ with the condition as y = 0 at x = 0. The value of y at x = 1.0 is ________ (rounded off to two decimal places).

Let y be the solution of the initial value problem y'' + 0.8y' + 0.16y = 0, where y(0) = 3 and y'(0) = 4.5. Then, y(1) is equal to ________ (rounded off to 1 decimal place).

Let $y$ be the solution of the initial value problem $y^{\prime}+0.8 y+0.16 y=0$ where $y(0)=3$ and $y^{\prime}(0)=4.5$. Then, $y(1)$ is equal to__________ (rounded off to 1 decima...

Consider the differential equation given below. Using the Euler method with the step size (h) of 0.5 , the value of $y$ at $x=1.0$ is equal to _________ (rounded off to 1 decimal p...

In the differential equation $\frac{dy}{dx} + \alpha xy = 0$, $\alpha$ is a positive constant. If $y = 1.0$ at $x = 0.0$, and $y = 0.8$ at $x = 1.0$, the value of $\alpha$ is _____...

In the differential equation $\frac{dy}{dx}+\alpha\ x\ y =0, \alpha$ is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is ________ (rounded off...

Consider the differential equation $${{dy} \over {dx}} = 4(x + 2) - y$$ For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a ste...

For the Ordinary Differential Equation $\frac{d^2x}{dt^2} - 5\frac{dx}{dt} + 6x = 0$, with initial conditions $x(0) = 0$ and $\frac{dx}{dt}(0) = 10$, the solution is

Consider the ordinary differential equation $x^2 \frac{d^2y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0$. Given the values of y(1) = 0 and y(2) = 2, the value of y(3) (round off to 1 decima...

The solution of the equation $x \frac{dy}{dx} + y = 0$ passing through the point (1,1) is

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

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

The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is

The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is

The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $$y=0$$ 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...

Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$

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...

Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}...